Physics | Physics and Universe https://physicsanduniverse.com Wed, 08 Jul 2026 05:11:30 +0000 en-US hourly 1 https://wordpress.org/?v=6.8.5 52870843 Writing equations with Latex https://physicsanduniverse.com/writing-equations-with-latex/ https://physicsanduniverse.com/writing-equations-with-latex/#respond Mon, 13 Jul 2026 04:48:27 +0000 https://physicsanduniverse.com/?p=10867 LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. LaTeX is the de facto standard for the communication and publication of scientific documents. LaTeX is available as free software. Latex has been widely used in the field of physics and mathematics where writing equations is a must. Latex is also available for web and can be used easily. I am also using latex to write equations on this site and wordpress plugin called jetpack come with the latex facility. All you have to do is install Jetpack plugin for wordpress and activate the plugin. That’s it. You are now ready to write beautiful mathematical equations. The aim of this post is to give code of some of the most popular equation that comes up in Math and Physics.

Latex inputResult
E = mc^2E = mc^2
\nabla q \nabla p \ge \dfrac{\hbar}{2}\nabla q \nabla p \ge \dfrac{\hbar}{2}
F = \dfrac{1}{4\pi\epsilon_0} \dfrac{Q_1Q_2}{r^2}F = \dfrac{1}{4\pi\epsilon_0} \dfrac{Q_1Q_2}{r^2}
g’ = g \sqrt{1 – \dfrac{2 \omega^2 R cos^2 \phi}{g}}g' = g \sqrt{1 - \dfrac{2 \omega^2 R cos^2 \phi}{g}}
b^2+p^2=h^2b^2+p^2=h^2
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
e^{i\pi}+1=0e^{i\pi}+1=0
F=G\frac{m_1m_2}{r^2}F=G\frac{m_1m_2}{r^2}
\nabla\cdot\mathbf{E}=\frac{\rho}{\varepsilon_0}\nabla\cdot\mathbf{E}=\frac{\rho}{\varepsilon_0}
E=h\nuE=h\nu
PV=nRTPV=nRT
e^{ix}=\cos x+i\sin xe^{ix}=\cos x+i\sin x
F(\omega)=\int_{-\infty}^{\infty}f(t)e^{-i\omega t}\,dtF(\omega)=\int_{-\infty}^{\infty}f(t)e^{-i\omega t}\,dt
\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}
v=f\lambdav=f\lambda
i\hbar\frac{\partial\Psi}{\partial t}=\hat{H}\Psii\hbar\frac{\partial\Psi}{\partial t}=\hat{H}\Psi
\int_a^b f'(x)\,dx=f(b)-f(a)\int_a^b f'(x)\,dx=f(b)-f(a)
]]> https://physicsanduniverse.com/writing-equations-with-latex/feed/ 0 10867 SI Units https://physicsanduniverse.com/si-units/ https://physicsanduniverse.com/si-units/#respond Sat, 31 Jul 2021 17:53:15 +0000 https://physicsanduniverse.com/?p=8984 General Conference on Weights and Measures in 1971 adopted seven quantities as fundamental base quantities. These seven base quantities are known as International System of units or SI in brief. There quantities listed below are seven fundamental quantities

QuantitySI UnitSymbol
Lengthmeterm
Masskilogramkg
Timeseconds
Electric currentampereA
TemperaturekelvinK
Amount of substancemolemole
Luminous intensitycandelacd

Two supplementary units are also added for Plane angle called radian (rad) and another unit for solid angle called steradian (Sr.)

Meter: One meter is defined as a distance between two lines engraved on a platinum-iradium bar kept at 0C at the International Bureau of Weights and measures at Paris. However a more accurate definition of meter is defined as distance traveled by light in vacuum in 1/299792458 second.

Kilogram: It is mass of cylinder made of platinum-iridium alloy kept at international Bureau of weight and measurements in Paris. With internationl agreement, mass of 1kg is assigned to it.

Second: One second is time taken to make 9,192,631,770 vibrations by a hyperfine transition in cesium-133 atom.

Ampere: It is current which when passed equally through two long parallel conductors kept one meter apart in vacuum, produces a force of 2 \times 10^{-7} newton/m on the wires.

Kelvin: It is 1/273.16 of the temperature of tripple point of water. The temperature of triple point of water is 273.16 kelvin.

Mole: It is the mass of a substance that contains 6.023 \times 10^{23} number of atoms or molecules. The number 6.023 \times 10^{23} is called Avogadro number. Example one mole of carbon-12 has a mass of 0.012kg exactly and contains 6.023 \times 10^{23} number of carbon atoms.

Candela: It is the luminous energy emitted per second by a source per unit solid angle. It has a radiant intensity of 1/683 watt per steradian.

Radian: It is the angle subtended at the center of a circle of radius r by an arc of length r of the same circle.

Solid Angle: It is defined as the angle subtended at a point by the surface area.

Steradian: It is the solid angle subtended at the center by unit area on the surface of a sphere of unit radius. Total solid angle subtended at the center by the surface area of a sphere of radius r in 4\pi steradian.

]]> https://physicsanduniverse.com/si-units/feed/ 0 8984 Solar constant and temperature of the Sun https://physicsanduniverse.com/solar-constant-and-temperature-of-the-sun/ https://physicsanduniverse.com/solar-constant-and-temperature-of-the-sun/#respond Sat, 13 Jun 2020 12:47:46 +0000 https://physicsanduniverse.com/?p=8887 Solar constant is the amount of energy received from the sun per second per unit area by a perfect black body on the earth, the area being placed normal to the direction of radiation.

Let S be the solar constant r be the distance of the earth from the sun and R be the radius of the sun.

Total energy radiated by the sun per second is \sigma T^4 \times 4 \pi R^2

Here T is the temperature of the sun and \sigma is the Stefan’s constant.

Energy received per second per unit are on the surface of the earth is

= \dfrac{\sigma T^4 \times 4 \pi R^2}{4 \pi r^2} = \dfrac{\sigma T^4 R^2}{r^2}

According to the definition of the solar constant, this is the solar constant.

S = \dfrac{\sigma T^4 R^2}{r^2}

T^4 = \dfrac{Sr^2}{\sigma R^2}

T = \left(\dfrac{Sr^2}{\sigma R^2}\right)^\frac{1}{4}

Hence by knowing the value of S, the temperature of the sun can be estimated.

]]> https://physicsanduniverse.com/solar-constant-and-temperature-of-the-sun/feed/ 0 8887 Motion down an inclined plane https://physicsanduniverse.com/motion-inclined-plane/ https://physicsanduniverse.com/motion-inclined-plane/#respond Sat, 23 Dec 2017 07:16:48 +0000 http://physicsanduniverse.com/?p=8642 Let P be a particle on a smooth plane inclined at an angle alpha to the horizon. If ABC represent a vertical section of the inclined planemotion down inclined plane through P, AB is the line of greatest slope and the angle ABC is alpha. The acceleration of P due to gravity is g and it is vertically downwards towards PQ. If PN be normal to the plane then angle QPN is alpha. The resolved parts of g are g cos\alpha along PN and g sin \alpha along PB.

Since the plane prevents any motion perpendicular to it, the particle moves down the plane along AB with acceleration g sin \alpha

If h be the height AC and l the length AB of the inclined plane sin \alpha = \dfrac{h}{l}

Let a particle slide down AB from rest and v be its velocity at B.

Then v^2 = 2gsin\alpha l = 2gh

Thus the velocity acquired is independent of alpha and is the same as the velocity acquired in falling through a height h.

If t be the time taken to slide down AB, l = \dfrac{1}{2}g sin\alpha t^2

t = \sqrt{\dfrac{2l}{g sin\alpha}}

If the particle is projected upwards along BA, its acceleration is -g sin\alpha

]]> https://physicsanduniverse.com/motion-inclined-plane/feed/ 0 8642 Motion under Gravity https://physicsanduniverse.com/motion-under-gravity/ https://physicsanduniverse.com/motion-under-gravity/#respond Sat, 16 Dec 2017 05:07:14 +0000 http://physicsanduniverse.com/?p=8629 When a body falls towards the earth we can notice that its velocity increases as it approaches earth. Hence the falling body is accelerating. Galileo performed several experiment and showed that falling bodies with different mass from same height reach the earth at the same time and hence they fall with constant acceleration. This acceleration is called acceleration due to gravity and is denoted by symbol g .

Experiments have shown that the value of g the same at the same place and varies slightly from place to place. A fairly correct value of g is 9.8 m/s^2 or 32 ft/sec^2 .

Vertically downward motion

A particle moving vertically downwards from height h goes downward with an acceleration g . If we take the downward directions as positive and replace s by h and a by g in equations of motion, we get

v = h + gt

h = ut + \dfrac{1}{2}gt^2

v^2 = u^2 + 2gh

Vertically upward motion

A particle thrown vertically upward moves with a retardation g . Its velocity slowly diminishes and becomes zero when the particle is at its maximum height. The body is then at rest for an instant and immediately begins to fall with acceleration g . We take upward direction as positive and replace g with -g then equations of motions becomes

v = u -gt

h = ut - \dfrac{1}{2} gt^2

v^2 = u^2 - 2gh

Greatest height and time of ascent when particle is thrown upward vertically

Let H be the maximum height attained in time T. Since velocity is 0 at the maximum height, 0 = u - gT and 0 = u^2 - 2gH

Time to reach the top: T = \dfrac{u}{g}

Maximum height reached: H = \dfrac{u^2}{2g}

Time of flight

When the particle returns to the earth, the vertical displacement is zero. If T’ is the time taken to come back, 0 = uT' - \dfrac{1}{2}gT'^2  = T'(u - \dfrac{1}{2} gT')

T' = 0

T' = \dfrac{2u}{g} this gives the total time of flight.

Since the time of ascent is \dfrac{u}{g} , time  of flight is twice the time of ascent.

So, time of ascent is equal to time of descent.

Time taken to reach a height of h

From h = ut - \dfrac{1}{2}gt^2

t = \dfrac{u \pm \sqrt{u^2-2gh}}{g}

When u^2 > 2gh , t has two real values which chows that particle reaches the height twice … once on its way up and once on its way down after it has reached the greatest height.

If h > \dfrac{u}{2g} or u^2 < 2gh , t becomes imaginary. It shows that the particle does not go higher than \dfrac{u^2}{2g}

Velocity at a height h

From v^2 = u^2 - 2gh we have

v = \pm \sqrt{u^2-2gh}

The positive value represents upward velocity and negative value represents downward velocity at the same height h. It shows that magnitude of the velocity is the same when the particle is at the same height whether it is ascending and descending.

]]> https://physicsanduniverse.com/motion-under-gravity/feed/ 0 8629 E equal to mc squared derivation https://physicsanduniverse.com/e-equal-mc-squared-derivation/ https://physicsanduniverse.com/e-equal-mc-squared-derivation/#respond Sat, 02 Dec 2017 14:24:45 +0000 http://physicsanduniverse.com/?p=8612 Here is how we derive mass energy equivalence

Force is defined as rate of change of momentum i.e.,

F = \frac{d}{dt}(m\nu) ….. (1)

According to the theory of relativity, both mass and velocity are variable. Therefore

F = \frac{d}{dt}(m\nu) = m \frac{d\nu}{dt} + \nu \frac{dm}{dt} ….. (2)

Let the force F displace the body through a distance dx. Then, the increase in the kinetic energy (dE_k) of the body is equal to the work done (Fdx) . Hence,

dE_k = F dx = m \frac{d\nu}{dt}dx + \nu \frac{dm}{dt}dx

or, dE_k = m\nu d\nu + \nu^2 dm ….. (3)

According to the law of variation of mass of velocity

m = \frac{m_0}{\sqrt{1-\frac{\nu^2}{c^2}}} ….. (4)

Squaring both sides, m^2 = \frac{m_0^2}{1-\frac{\nu^2}{c^2}}

or, m^2c^2 = m_0^2c^2 + m^2\nu^2

Differentiating,

c^2 2m dm = m^2 2\nu d\nu + \nu^2 2m dm

or, c^2 dm = m\nu d\nu + \nu^2 dm ….. (5)

From equation (3) and (5)

dE_k = c^2 dm ….. (6)

Thus, a change in K.E. dE_k is directly proportional to a change in mass  dm. When a body is at rest, its velocity is zero, (K.E. = 0) and m = m_0 . When its velocity is \nu , its mass becomes m. Therefore, integrating equation (6)

E_k = \int_0^{E_k}dE_k = c^2 \int_{m_0}^{m} dm = c^2(m-m_0)

Therefore, E_k = mc^2 - m_0c^2 ….. (7)

This is the relativistic formula for K.E. When the body is at rest, the internal energy stored in the body is m_0c^2 . m_0c^2 is called the rest mass energy. The total energy (E) of the body is the sum of K.E. (E_k) and rest mass energy m_0c^2

So, E = E_k + m_0c^2 = (mc^2 - m_0c^2) + m_0c^2 = mc^2

This is Einstein’s mass energy relation.

This relation states a universal equivalence between mass and energy. It means that mass may appear as energy and energy as mass.

The relationship E = mc^2 between energy and mass forms the basis of understanding nuclear reactions such as fission and fusion. These reactions take place in nuclear bombs and reactors. When a uranium nucleus is split up, the decrease in its total rest mass appears in the form of an equivalent amount of K.E. of its fragments.

]]> https://physicsanduniverse.com/e-equal-mc-squared-derivation/feed/ 0 8612 The General Theory of Relativity https://physicsanduniverse.com/general-theory-relativity/ https://physicsanduniverse.com/general-theory-relativity/#respond Sat, 25 Nov 2017 14:17:15 +0000 http://physicsanduniverse.com/?p=8607 The special theory of relativity is valid only for inertial systems i.e.  Systems moving with constant relative velocity.  According to the first postulate of special relativity “the laws of physics may be expressed in equations having the same form in all frames of reference moving at constant velocity with respect to one another”. The corresponding postulate of general relativity states that “the laws of physics may be expressed in equations having the same form in all frames of reference, regardless of their states of motion”. Thus the general theory covers accelerated as well as uniform motion. Hence it is able to describe gravitational phenomena.

The second postulate of general relativity states that there is no way for an observer in a closed laboratory to distinguish between the effects produced by a gravitational field and those produced by an acceleration of the laboratory. This postulate is known as the principle of equivalence. This postulate follows from the experimental observation that the inertial mass of a body is always exactly equal to its gravitational mass.

Einstein generalized the principle of equivalence and proposed that the physical laws have similar mathematical forms not only in inertial systems but in accelerated system also. According to him the idea of action at a distance of exploration of gravitation is false and by selecting a suitable coordinate system, the effect of gravitation can be eliminated. In this system the inertial mass of body is equal to its gravitational mass. To explain these ideas, let us consider the weight of a body in a lift. If the lift goes upwards with an acceleration a, the weight of the body is m(g+a) . If the lift goes down with acceleration a, the weight of the body is m(g-a) . If the lift goes down with acceleration g, the weight of the body will be zero. Hence the gravitational effect on the body depends on the state of the lift.

Einstein theory of gravitation have given some prediction and the three main successes are given below:

  1. Effect of gravitational field on a ray of light: Inertial mass \frac{h\nu}{c^2} so that light ought to be subject to gravitational forces. For example, light rays that pass near the sun ought to be deflected towards it, just as the paths of the planets are deflected by the sun’s gravitational field. This deflection is known as “Einstein effect“. This effect can be detected at the time of total solar eclipse.
  2. The general theory predicts that the path of a planet about the sun will not be precisely an ellipse. The orbit will slowly rotate in the plane of its motion, so that the axes turn in space in the same sense as the planet’s rotation. For the planets in our solar system, this effect should be just sufficiently great to be observed in the case of Mercury, which passes closest to the sun. The point of the orbit at which the planet is nearest to the sun is called the ‘perihelion’. The perihelion itself is found to be very slowly rotating around the sun. This effect is called the ‘advance of the perihelion’ of Mercury. Observed and predicted values of this rotation of the planet’s orbit 2 \times 10^-4 rad. per.century agree to within the accuracy of astronomical measurement.
  3. The third prediction of general relativity is that a stationary clock runs more slowly in a strong gravitational field than in a weak one. Suppose a clock has an interval of t between ticks when it is infinitely far from all matter. When the clock is at a distance R from a mass M, then it will have an interval of t=T_0\sqrt{1-\frac{2GM}{R}}   between ticks. An atom emitting light of a definite frequency is equivalent to a clock (atomic clock). The third prediction means that the light emitted by an atom on a star must be of frequency lower than that emitted by the same atom on earth (since the gravitational field of star is much more stronger than that of earth). In other words, the light from the star must be shifted towards the red end of the spectrum (apart from any Doppler’s shift). This effect is called the “gravitational red shift”. The gravitational red shift has been actually observed in the spectral lines of certain stars called ‘white dwarfs’ and also in a laboratory experiment involving “Mossbauer effect” and has verified the prediction.
]]> https://physicsanduniverse.com/general-theory-relativity/feed/ 0 8607 Special Relativity https://physicsanduniverse.com/special-relativity/ https://physicsanduniverse.com/special-relativity/#comments Tue, 17 May 2016 07:38:38 +0000 http://physicsanduniverse.com/?p=8437 In 1905 Albert Einstein purposed how measurement of time and space are affected by motion between an observer and the object that is being observed. He called this theory the theory of Relativity and there are Special theory of relativity and General theory of relativity and both theories were worked out by Einstein. We will talk about Special theory of relativity today.

Special relativity states that All motions is relative; the speed of light in free space is the same for all observers.

There are few things we need to understand before we dive into special relativity. Firstly, what do we mean by motion? Motion is defined as change in an object’s position relative to something else. For example, an airplane moves relative to the earth, our sun moves relative to our galaxy etc. In each case we can see that the frame of reference is a something which is a part of the description of the motion.

An inertial frame of reference is one where Newton’s first law of motion holds true that is an object at rest remains at rest and object in motion will continue to be in motion at constant velocity of no force is acted upon it. You must have noticed that when you are in a bus or train the trees in the distance seems to move with respect to us. So, the question arises is it moving or we are moving? A relative motion is hard to grasp and understand. It is to be noted here that there is no universal frame of reference that can be used everywhere. Hence special theory of relativity deals with this lack of universal frame of reference and problems that involves inertial frames of reference. General relativity on the other hand deals with accelerated frame of reference with one another.

Postulates of Special Relativity

  1. The laws of Physics are the same in all inertial frame of reference. (this postulates arises from the absence of universal frame of reference)
  2. The speed of light in free space has the same value in all inertial frame of reference.
]]> https://physicsanduniverse.com/special-relativity/feed/ 1 8437 How to supercool water https://physicsanduniverse.com/how-to-supercool-water/ https://physicsanduniverse.com/how-to-supercool-water/#respond Tue, 11 Nov 2014 06:23:26 +0000 http://physicsanduniverse.com/?p=7801 At normal atmospheric pressure, water freezes at zero degrees Celsius and boils at 100 degrees. It is to be noted that the freezing and boiling points of water are how we define the Celsius temperature system. But as always there are some exceptions and as it turns out water doesn’t always freeze at zero degree Celsius. At some conditions we can put a bottle of water in the freezer for hours and it will remain liquid unless we do something.

Here liquids are subjected to a special state called super cooling and it is the state where liquid doesn’t solidify even if it is below the freezing point. Liquids needs something become solid at a certain temperature because there is a process which involves the lineup of molecules. All states of matter solid, liquid, or gas at constant pressure depends on its energy or heat. In a gas, molecules are warmer, and are higher in energy. They move a lot, fly everywhere and collide with each other often. But in a liquid, molecules don’t have as much energy as compared to gas and move around slow enough to form a bonds between them, keeping them close together. At lower temperatures, where molecules have the least amount of energy, they forma solid. They’re still vibrating a bit, but at this point the bonds between them keep the molecules rigidly in place.

In order to freeze water, it should have low energy meaning it should be cold and it should form intermolecular bonds holding it as a solid. To make this bond water has to form a nucleus around which the cool water will for ice eventually. This point is called nucleation site it is the place where structure of ice crystal begins to form. This then allows other water molecules around it to form bonds eventually expanding to make one solid piece of ice. This nucleation sites needs to be created and this creation of nucleation is generally helped by impurities in water. This impurities might be a mineral present in water. Nucleation site can also be created by disturbing the super cooled liquid like shaking. As the very cold water moves around cool molecules will and start the process of turning into ice. So to create super cool water, you have to keep impurities and movement as far as possible.

How to supercool water

To make super cool water you need a freezer and a bottle of standard drugstore-brand purified water. Mineral water is useless as it contains things that will act as a nucleation sites. Keep your bottle of water in the freezer. Keep it in the freezer for about two and a half hours and make sure that you don’t open the freezer because we want gradual cooling and opening the freezer might disturb and gradual cooling process. If everything went well, you will have a supercooled below-freezing liquid water. If you slam this bottle of supercooled water against the table, you will create a nucleation site, and you can actually see the ice crystal form almost instantly. Which is SUPER COOL!

]]> https://physicsanduniverse.com/how-to-supercool-water/feed/ 0 7801 Units and measurement https://physicsanduniverse.com/units-measurement/ https://physicsanduniverse.com/units-measurement/#respond Thu, 10 Apr 2014 06:46:38 +0000 http://physicsanduniverse.com/?p=606 The 14th general conference on weight and measurement in 1971 decided seven fundamental quantities as basic quantities. These seven unit of measurement are known as the International System of units along with two supplementary units. Its abbreviated as SI from its french name. This system of unit is mostly used by most of the book and has been in use throughout the world extensively.

S.No. Quantity SI unit Symbol
1 Length meter m
2 Mass kilogram kg
3 Time second s
4 Electric current ampere A
5 Temperature kelvin K
6 Amount of substance mole mole
7 Luminous intensity candela cd
8 Plane angle radian rad
9 Solid angle steradian Sr

Meter: One meter is distance between two lines on a platinum iridium bar kept at zero degree Celsius at International Bureau of Weights and Measurements at Sevres, Paris. A more accurate definition of meter is the distance traveled by light in vacuum in \frac{1}{2997922458} second.

Kilogram: A standard kilogram is an agreed upon mass of cylinder made up off platinum iridium alloy kept at International Bureau of Weights and Measurements in Paris.

Second: One second is defined as the time taken to make 9,192,631,770 vibrations by a hyperfine transitions in Cesium-133 atom.

Kelvin: It is \frac{1}{273.15} of the temperature of triple point of water. The temperature of triple point of water is 273.15 Kelvin.

Mole: Mole is defined as the mass of the substance that contains 6.02252 \times 10^{23} number of atoms or molecules. The number 6.02252 \times 10^{23} is called Avogadro number.

Candela: It is the luminous energy emitted per second by a source per unit solid angle. It has a radiant intensity of \frac{1}{683} watt per steradian.

Radian: It is an angle subtended at the center of a circle of radius r by an arc of length r of the same circle.

1 radian = \frac{Arc}{radius}

Note that: 2\pi radians = 360 degree

Solid angle: It is the angle subtended at a point by the surface area.

Solid-angle = \frac{Area-of-surface}{(distance-of-point-from-the-surface)^2}

\Omega = \frac{A}{x^2}

Steradian: It is the solid angle subtended at the center by unit area on the surface of a sphere of unit radius. Total solid angle subtended at the center by the surface area of a sphere of radius r is 4\pi steradian.

Prefixes of power of Ten
S.No. Power of 10 Prefix Symbol
1 10^{18} exa- E
2 10^{15} peta- P
3 10^{12} tera- T
4 10^{9} giga- G
5 10^{6} mega- M
6 10^{3} kilo- k
7 10^{2} hecto- h
8 10 deka- da
9 10^{-1} deci- d
10 10^{-2} centi- c
11 10^{-3} milli- m
12 10^{-6} micro- \mu
13 10^{-9} nano- n
14 10^{-12} pico- p
15 10^{-15} femto- f
16 10^{-18} atto- a

]]> https://physicsanduniverse.com/units-measurement/feed/ 0 606 Temperature of Earth without Atmosphere https://physicsanduniverse.com/temperature-of-earth-without-atmosphere/ https://physicsanduniverse.com/temperature-of-earth-without-atmosphere/#respond Tue, 28 May 2013 17:22:50 +0000 http://physicsanduniverse.com/?p=46 EarthTemperature of Earth without Atmosphere

During the day time, when the heat radiation from the sun comes towards the earth, they are reflected back into space by the earth’s atmosphere. As a result, only some amount of heat radiation is able to reach the earth. During the night, the earth radiates heat which is reflected back to the surface by the atmosphere. It is therefore, if there were no atmosphere, all of the heat radiation from the sun would reach Earth and the Earth would be inhospitably hot in the day time. On the other hand, all of the heat radiated by the earth in the night time would escape into the space thus leaving the earth inhospitably cold.

Anomalous expansion of water

Unlike other liquids, water shows unusual expansion which is called anomalous expansion of water. When temperature of water decreases from 100 C, volume of the water also decreases and hence the density increases. The volume of water becomes minimum at 4 C. If the temperature is further reduced to zero, the volume of water again expands. In further cooling from 0 C, ice contracts normally. Thus the water has maximum density at 4 C.

Small space is left between two rails on a railway track

The rail may be heated due to (i) the high temperature on summer and (ii) the heat caused by the friction between the wheels and the track. Due to these heating, the rails get expanded and enough space is to be left for the expansion of the rails, otherwise the railway track may be curved during expansion and may be displaced from the original track. Hence, the spaces are left between the rails of a railway track.

Mercury is used as a thermometric substance

Mercury has uniform expansion and it does not wet the glass tube. Therefore, mercury is mostly used as the thermometric substance.

]]> https://physicsanduniverse.com/temperature-of-earth-without-atmosphere/feed/ 0 46