# Important laws of physics in detail

In this particular article we are going to discuss some important laws of physics in detail. We will discuss Kirchhoff’s law, Wien’s displacement law, gas law, Newton’s law of cooling, Avogadro’s law, Dalton’s law, Grahm’s law, kinetic theory of an ideal gas, degree of freedom etc.

## Kirchhoff’s law

If different bodies (including a perfectly black body) are kept at same temperature, then emissive power is proportional to the absorption power.

e ∝ a or e / a = constant

Or (e/a)body 1 = (e/b)body 2 = (e/a) perfectly black body

- Good absorber od a particular wavelength λ are also good emitters of same wavelength.
- At a given temperature, ratio of e and a for any body is constant. This ratio is equal to e of perfectly black body at that temperature.

### Wien’s displacement law

λm ∝ 1/T or λmT = constant = Wien’s constant (b)

Here b= 2.89 × 10¯³ mK

Futher, area of this graph will give total emissive power which is proportional to Tˆ4.

Cooling of a body by radiation

Rate of cooling

-dT/dt = eAσ( Tˆ4 – Tοˆ4)/ms

Or -dT/dt ∝ (Tˆ4 – Toˆ4)

#### Gas law

These mostly are of three types-

- Boyle’s law
- Charles law
- Gay-Lussac’s law

##### Newton’s law of cooling

1. If temperature difference of a body with atmosphere is small, then rate of cooling is proportional to the temperature difference.

2. If body cools by radiation according to this law, then temperature of body decreases exponentially. In the figure,

Ti = initial temperature of body

T₀ = temperature of surrounding

Temperature at any time t can be written as,

T = T₀ + (Ti – T₀)eˆ¯kt

Where K is constant.

3. If body is cooling according to this law then to find temperature of a body at any time t, we will have to calculate eˆ-αt. To avoid this, you can use a shortcut approximate formula given below

(T₁- T₂)/t = k( (T₁ + T₂ /2)- T₀)

4. If in (T-T₀) be plotted against t, then the equation assumes the form y= mx+ c; where m =-k and C= ln(T₁ -T₀)

This is straight line with negative slope.

- If Qemission > Qabsorbtion → temperature of body decreases and consequently the body appears colder.
- And if Qemission < Qabsorbtion → temperature of body increases and it appears hotter.

If Qemission = Qabsorbtion → temperature of body remains constant (thermal equilibrium).

###### Avogadro’s law

At same temperature and pressure equal volumes of all gases contains equal number of molecules.

N₁ = N₂ ; if P, V and T are same.

###### Dalton’s law

According to this law, the pressure exerted by a mixture of several gases equals the sum of the pressure exerted by each component of gas present in the mixture i.e., Pmix = P₁ + P₂ + P₃….

P = (RT/V)(n₁ + n₂+ n₃+….)

###### Grahm’s law of diffusion

According to this law, at same temperature and pressure, the rate of diffusion of gases inversely proportional to the square root of the density of gas i.e.,

Rate of diffusion r∝ 1/√ρ

Also, υ ∝ 1/√ρ; so υ ∝ r

Kinetic theory of an Ideal Gas

1. Pressure of an Ideal gas inside the container

P = mNυ² / 3V = ρυ²/3

Where, m = mass of each molecule, N = total number of molecules, V = volume of container or total volume of gas, ρ = density of gas , υ = root mean square speed of gas.

2. Various types of speed of gas molecules

(a) Root mean square speed,

υ = √3P/ρ = √3RT/M = √3kT/m

Here, M= molar mass of the gas.

(b) Most probable speed

υ = √2P/ρ = √2RT/ M = √2kT/m

(c) Average speed

υ = √8P/πρ = √8RT/πM = √8kT/πm

(3) Kinetic energy of gas (internal energy)

1. Translatory kinetic energy

E = 1/2(Nmυ²) = 3PV/2

Total internal energy of an ideal gas is kinetic.

2. Energy per unit volume or energy density (Ev)

Ev = Total energy/volume

4. Molar K.E. or mean molar K.E. (E) : K.E. of N molecules

E = 3RT/2 = 3NkT/2

5. Molecular kinetic energy or mean molecular K.E. (E‾) : K.E. of a gas molecule

E‾ = E/N or E‾ = 3RT/ N ⇒E‾ = 3kT/2

Degree of freedom

- The number of independent ways in which a molecule or an atom can exhibit motion is called its degree of freedom.
- The number of independent coordinates required to specify the dynamical state of system is called its degree of freedom.
- The degree of freedom are of three types :

- Translation degree of freedom: Maximum three degree of freedom are there corresponding to translational motion.
- Rotational degree of freedom: The number of degrees of freedom in this case depends on the structure of the molecule.
- Vibrational degree of freedom: It exhibits at high temperature.

###### Conclusion

In this article we have studied some important laws of physics in easiest way possible. Hence now we are able to conclude that these laws have an great importance in field of physics.