B M Sharma Solutions for Chapter: Thermodynamics, Exercise 3: Exercises

In the given elliptical $P-V$ diagram

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. What is. the molar specific heat at constant pressure of mixture ?

The indicator diagram for two process $1$ and $2$ carried on an ideal gas is shown in figure. If $m_1$ and $m_2$ be the slopes $\left(\frac{\mathrm{d}P}{\mathrm{d}V}\right)$ for process $1$and process $2$ respectively, then:-

A thermally insulated chamber of volume $2V_0$ is divided by a frictionless piston of area $S$ into two equal parts $\mathrm{A}$ and $\mathrm{B}$. Part $\mathrm{A}$ has an ideal gas at pressure $P_0$ and temperature $T_0$ and in part $\mathrm{B}$ is vacuum. A massless spring of force constant $k$ is connected with piston and the wall of the container as shown. Initially spring is unstarched. Gas in chamber $\mathrm{A}$ is allowed to expand. Let in equilibrium spring is compressed by $x_0$ . Then

Calculate the heat absorbed by a system in going through the cyclic process shown in the given figure.

(Take $\pi =3.14$)

$A$ gas undergoes a change of state during which $100 \mathrm{J}$ of heat is supplied to it and it does $20 \mathrm{J}$ of work. The system is brought back to its original state through a process during which $20 \mathrm{J}$ of heat is rejected by the gas. Find the work done by the gas in the second process in joules.

A sample of an ideal gas is taken through a process $ABCD$. It absorbs $50 \mathrm{J}$ of energy during the process $AB$ which is an isometric process, no heat during $BC$ and it rejects $70 \mathrm{J}$ of heat during isobaric process $CD$. It is also given that $40 \mathrm{J}$ of work is done on the gas during the process $BC$. Internal energy of gas in state $A$ is $1500 \mathrm{J}$. Find the internal energy of gas in state $C$ in joules.

A gas consisting of rigid diatomic molecules was expanded $ma$ polytropic process so that the rate of collisions of the molecules against the vessel's wall did not change. Find the molar heat capacity of the gas in this process in $\mathrm{J}/\mathrm{mol}-\mathrm{K}$. (Given: Gas constant $R=8.3 \mathrm{J}/\mathrm{mol}-\mathrm{K}$)