Q.Give an equation of state for an isochoric process.

In an isochoric (constant-volume) process, no work is done by or on the gas, so W = 0.

The work done by a gas during a small volume change is dW = P dV. In an isochoric process, the volume is held fixed, so dV = 0 throughout the process, which means

W = integral of P dV = 0

This is the defining mechanical consequence of constant volume: even though pressure and temperature can change (e.g., by heating the gas in a rigid, sealed container), and heat Q can flow in or out (going entirely into changing internal energy, by the first law: Q = delta U since W = 0), no work is exchanged with the surroundings simply because the boundary of the gas does not move.

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