Question

An ideal gas has initial volume $V$ and pressure $p$. If the volume of gas is doubled during expansion, then minimum work will be done in which thermodynamic process ?

• A. Isobaric process
• B. Isothermal process
• C. Adiabatic process
• D. Same in all alone given process

Answer 1

The correct option is C Adiabatic process

$W_{gas}=\int PdV$
Hence work done by gas in each process can be compared by estimating the area under their respective $P-V$ graphs.


Plotting the $P-V$ curve for the given isobaric, isothermal, adiabatic processes for expansion of gas from $V\to 2V$.
$\because {\text{slope}}_{\text{Adiabatic}}>{\text{slope}}_{\text{Isothermal}}$
Hence, curve of adiabatic process will be more steep compared to that of isothermal one.

we get the following order for area under curve:
$A_{\text{Isobaric}}>A_{\text{Isothermal}}>A_{\text{Adiabatic}}$
$\Rightarrow W_{\text{Isobaric}}>W_{\text{Isothermal}}>W_{\text{Adiabatic}}$
Hence, minimum work is done by gas in adiabatic process.