Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 1: Exercise-1

The expansion of unit mass of a perfect gas at constant pressure is shown in the diagram. Here:

Air is filled at $60°\mathrm{C}$ in a vessel of open mouth. The vessel is heated to a temperature $T$ so that $\frac{1}{4}\mathrm{th}$ part of air escapes. The value of $T$ is:

One mole of an ideal gas undergoes a process $P=\frac{P_0}{1+{\left(V_0/V\right)}^2}$, here $P_0$ and $V_0$ are constants. Change in temperature of the gas when the volume is changed from $V=V_0$ to $V=2{\mathrm{V}}_0$ is:

From the following $V-T$ diagram we can conclude:

A gas is expanded from volume $V_0$ to $2{\mathrm{V}}_0$ under three different processes. Process $1$ is isobaric process, Process $2$ is isothermal and Process $3$ is adiabatic. Let $∆U_1, ∆U_2$ and $∆U_3$, be the change in internal energy of the gas is these processes. Then:

The internal energy  of a gas in an adiabatic process is given by $U=a+bPV$, find $\gamma :$

What would be the efficiency of the heat engine diagramed as shown below?

An ideal Carnot heat engine with an efficiency of $30\%$. It absorbs heat from a hot reservoir at $727°\mathrm{C}$. The temperature of the cold reservoir is