Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 1: WBJEE 2020

Consider the given diagram. An ideal gas is contained in a chamber (left) of volume $V$ and is at an absolute temperature $T.$ It is allowed to rush freely into the right chamber of volume $V$ which is initially vacuum. The whole system is thermally isolated. What will be the final temperature, if the equilibrium has been attained?

Which of the following statements(s) is/are true?
"Internal energy of an ideal gas.........

What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points $\left(V_0,T_0\right)$ and $\left(2V_0,3T_0\right)$ in a $V-T$ diagram. What is the value of the heat capacity of the gas at the point $\left(V_0,T_0\right)?$

An ideal gas undergoes the cyclic process $abca$ as shown in the given $p-V$ diagram.

It rejects $50 \mathrm{J}$ of heat during $ab$ and absorbs $80 \mathrm{J}$ of heat during $ca$. During $bc$, there is no transfer of heat and $40 \mathrm{J}$ of work is done by the gas. What should be the area of the closed curve $abca ?$

The initial pressure and volume of a given mass of an ideal gas with $\left(\frac{C_p}{C_V}=\gamma \right)$, taken in a cylinder fitted with a piston, are $p_0$ and $V_0$ respectively. At this stage the gas has the same temperature as that of the surrounding medium which is $T_0.$ It is adiabatically compressed to a volume equal to $\frac{V_0}{2}.$
Subsequently the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surrounding?

For an ideal gas with initial pressure and volume $p_i$ and $V_i$ respectively, a reversible isothermal expansion happens, when its volume becomes $V_0$. Then, it is compressed to its original volume $V_i$ by a reversible adiabatic process. If the final pressure is $p_f$ then which of the following statement(s) is/are true?

Consider an engine that absorbs $130 \mathrm{cal}$ of heat from a hot reservoir and delivers $30 \mathrm{cal}$ heat to a cold reservoir in each cycle. The engine also consumes $2 \mathrm{J}$ energy in each cycle to overcome friction. If the engine works at $90$ cycles per minute, what will be the maximum power delivered to the load? [Assume the thermal equivalent of heat is $4.2 \mathrm{J}/\mathrm{cal}$]