Question

If a certain mass of gas is made to undergo separately adiabatic and isothermal expansion to the same pressure, starting from the same initial condition of temperature and pressure, then, as compared to that of isothermal expansion, in the case of adiabatic expansion, the final

• A. volume and temperature will be higher
• B. volume and temperature will be lower
• C. temperature will be lower but the final volume will be higher
• D. volume will be lower but the final volume will be higher

Answer 1

The correct option is C temperature will be lower but the final volume will be higher

We know for an adiabatic process,
$P_1{V}_1^{\gamma }$ = $P_2{V}_2^{\gamma }$
For an isothermal process,
$P_1{V}_1$ = $P_2{V}_2$
Given, Initial temperatures, pressures,and volumes and final pressures are same for both the processes.
For an adiabatic process,
$P_1{V}_1^{\gamma }$ = $P_2{V}_2^{\gamma }$...........(1)
where $V_2$ is the final volume for an adiabatic process

For an isothermal process,
$P_1{V}_1$ = $P_2{V}_3$.............(2)
where $V_3$ is the final volume for an isothermal process.
The ratio of (1) and (2)

1= $\frac{V_2^{\gamma }}{V_3}$
since $\gamma$ is greater than 1, $V_3$ must be greater than $V_2$
similarly,
For an adiabatic process,
$P_1^{1-\gamma }{T}_1^{\gamma }=P_2^{1-\gamma }{T}_2^{\gamma }$
Temperature decreases with pressure.
For an isothermal process,
Initial and final temperature will be same.
$T_2<T_1$