The reason why the volume is constant in an isochoric process and no work is done is because the volume change is zero, in this case, the work done is zero.
The work done by an ideal gas is defined as its pressure times its change in volume, or PΔV (or PdV). Because the volume change ΔV, is zero in an isochoric process, however, no work is done by the gas. Hence, the change in internal energy of the gas is simply equal to the amount of heat added.
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Answer:
The work done by an ideal gas is defined as its pressure times its change in volume, or PΔV (or PdV). Because the volume change ΔV, is zero in an isochoric process, however, no work is done by the gas. Hence, the change in internal energy of the gas is simply equal to the amount of heat added.