Import Question JSON

$\text{The work done by a gas during expansion or compression is given by the integral:}\n\n$\text{W} = \int \text{PdV}\n\n\text{where P is the pressure and dV is the change in volume.}\n\n\text{1. Isochoric Process:}\n\text{In an isochoric process, the volume of the gas remains constant, which means dV = 0.}\n\text{Therefore, the work done (W) is zero.}\n\text{W} = \int \text{P}(0) = 0\n\text{This is the minimum possible work a gas can perform during expansion, as it is zero.}\n\n\text{2. Isobaric Process:}\n\text{In an isobaric process, the pressure (P) is constant. The work done is:}\n\text{W} = \text{P} \int \text{dV} = \text{P}(\text{V}_\text{final} - \text{V}_\text{initial})\n\text{Since the gas is expanding, } \text{V}_\text{final} > \text{V}_\text{initial}\text{, so the work done is positive and non-zero.}\n\n\text{3. Adiabatic Process:}\n\text{In an adiabatic process, there is no heat exchange with the surroundings. The work is done at the expense of the internal energy of the gas. The work done is positive during expansion, but less than in an isobaric or isothermal process because the temperature of the gas drops, reducing the pressure and thus the work output.}\n\n\text{4. Isothermal Process:}\n\text{In an isothermal process, the temperature remains constant. The work done is positive and non-zero during expansion.}\n\n\text{Comparing the work done in each process, the minimum work is done when dV=0, which occurs in an isochoric process. The work done in an isochoric expansion is exactly zero, which is the absolute minimum.}$