Tshering Dorji : Reflection on Class Test

Friday, 7 April 2023

Reflection on Class Test

Class Test😨

Hello friends, hope you all have done your Thermal Physics Mid-Term Exam up to your satisfaction. Today I am writing on Reflection on Class Test. I tried my best to answer all question but after comparing answers with my friends-BIG BRAIN people 😆, my answers were wrong. Just give a blink on what I have written on my Blog👀 I will try my best to Explain some Concepts we have to use while solving Mid-Term Exam of Thermal Physics

Basically, Question 1 ask us to prove the probability of a molecule having x component of velocity in the range u and u+du is given as

Here in this problem, we have to understand the concept of Maxwell-Boltzmann Velocity Distribution Law.

Maxwell Boltzmann
Maxwell-Boltzmann distribution, also called Maxwell distribution, a description of the statistical distribution of the energies of the molecules of a classical gas. This distribution was first set forth by Scottish
physicist James Clerk Maxwell in 1859, on the basis of probabilistic arguments, and gave the distribution of velocities among the molecules of a gas. Maxwell’s finding was generalized (1871) by German physicist Ludwig Boltzmann to express the distribution of energies among the molecules.

Not all of the air molecules that surround us move at the same rate. Some air molecules move quickly, while others move slowly. As a result, rather than asking about the speed of each specific gas molecule, we ask about the distribution of speed in a gas at a certain temperature. James Maxwell and Ludwig Boltzmann devised a hypothesis to explain how the speeds of molecules are distributed in an ideal gas. The following graph is commonly used to show the distribution.

Maxwell-Boltzmann Distribution Law

Moving onto the Question 2, we are to find the relation between heat capacity at constant volume and heat capacity at constant pressure.

Julius Robert Mayer, a German chemist and physicist, derived a relation between specific heat at constant pressure and the specific heat at constant volume for an ideal gas. He

Julius Robert Mayer

9 studied the fact that the specific heat capacity of a gas at constant pressure (Cp) is slightly greater than at constant volume (Cv). He reasoned that this Cp is greater than the molar specific heat at constant volume Cv, because energy must now be supplied not only to raise the temperature of the gas but also for the gas to do work because in this case volume changes. According to the Mayer’s relation or the Mayer’s formula the difference between these two heat capacities is equal to the universal gas constant, thus the molar specific heat at constant pressure is equal to:

So, above equation is called as Mayer's Formula.

Mayer 's formula gives the relationship between molar specific heat of a gas at constant volume and pressure Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1° C. We symbolize it as C.

Cv (Molar specific heat at constant volume):- It is defined as the amount of heat required to increase the temperature of 1 mole of a gas through 1°C at constant volume. it is denoted by Cp.

Cp (Molar specific heat at constant pressure):- It is defined as the amount of heat required to increase the temperature of 1 mole of gas through 1°C at constant volume. it is denoted by Cp.

R (gas constant):- R is the universal gas constant for one mole of gas. As R is always positive, it follows that Cp > Cv.

Read more: Mayer's formula Derivation

The above relation is derived in above link.

Moving to third question, we are asked to differentiate between ideal and non-ideal gas.

For fifth question, we know that Pressure Correction of Van der Waal's is given as;

where a is the Van der Waal's Constant

Here we are ask to find the value of constant b in the equation in terms of specific volume at critical point Vc. We can find the value of constant b by finding the relationship between Tc,Vc and Pc in terms of a and b.