G L Mittal and TARUN MITTAL Solutions for Chapter: Internal Energy : First Law of Thermodynamics : Specific Heat, Exercise 1: QUESTIONS

The adjoining diagram shows the pressure-volume graph of thermodynamic processes of an ideal gas. Determine the work done in $\mathrm{A}\to \mathrm{B}, \mathrm{B}\to \mathrm{C} \mathrm{and} \mathrm{C}\to \mathrm{A}$ processes separately and the work done in the complete cycle $\mathrm{ABCA}.$

In the adjoining diagram are shown the changes taking place in a thermodynamic system in going from the initial state $\mathrm{A}$ to the states $\mathrm{B}$ and $\mathrm{C}$ and finally returning to the state $\mathrm{A}.$ If ${\mathrm{U}}_{\mathrm{A}}=30$ joule, ${\mathrm{U}}_{\mathrm{C}}=70$ joule and the heat spent in the change from state $\mathrm{A}$to $\mathrm{B}$ is $60$ joule, then determine work done by the system in the change from $\mathrm{B}$to $\mathrm{C}$.

In the adjoining diagram are shown the changes taking place in a thermodynamic system in going from the initial state $\mathrm{A}$ to the states $\mathrm{B}$ and $\mathrm{C}$ and finally returning to the state $\mathrm{A}.$ If ${\mathrm{U}}_{\mathrm{A}}=30$joule, ${\mathrm{U}}_{\mathrm{C}}=70$joule, and the heat spent in the change from state $\mathrm{A}$ to $\mathrm{B}$ is $60$ joule, then determine heat released from the system in the change from $\mathrm{C}$ to $\mathrm{A}$.

In the adjoining diagram are shown the changes taking place in a thermodynamic system in going from the initial state $\mathrm{A}$ to the states $\mathrm{B}$ and $\mathrm{C}$ and finally returning to the state $\mathrm{A}.$ If ${\mathrm{U}}_{\mathrm{A}}=30$ joule, ${\mathrm{U}}_{\mathrm{C}}=70$ joule and the heat spent in the change from state $\mathrm{A}$ to $\mathrm{B}$ is $60$ joule, then determine the value of ${\mathrm{U}}_{\mathrm{B}}$.

The initial pressure and volume of a gas are ${\mathrm{P}}_{\mathrm{i}} \mathrm{and} {\mathrm{V}}_{\mathrm{i}}$ respectively. They are increased to ${\mathrm{P}}_{\mathrm{f}} \mathrm{and} {\mathrm{V}}_{\mathrm{f}}.$ In which process will more work have to be done : (1) first increasing the volume only and increasing the pressure, or (2) first increasing the pressure only and then increasing the volume? Will the change in internal energy of the gas in these process be different?

Why is internal energy $\left(\mathrm{U}\right)$ said to be a unique function?

Prove that the difference in the molar specific heats $\left({\mathrm{C}}_{\mathrm{p}}, {\mathrm{C}}_{\mathrm{v}}\right)$ of an ideal gas is nearly $2 \mathrm{cal} {\mathrm{mol}}^{-1} {\mathrm{k}}^{-1}.$ Given : $\mathrm{R}=8.31 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}.$               

What is meant by 'degrees of freedom' of a gas molecule?