, V ) to the final state ( P , V ). At any intermediate stage with pressure P and volume change from V to V + ∆ V ( ∆ V small) ∆ W = P ∆ V Taking ( ∆ V → ) and summing the quantity ∆ W over the entire process, W = P d ∫ = RT RT d ∫ In ( . ) where in the second step we have made use of the ideal gas equation PV = µ RT and taken the constants out of the integral. For an ideal gas, internal energy depends only on temperature.
Thus, there is no change in the internal energy of an ideal gas in an isothermal process. The First Law of Thermodynamics then implies that heat supplied to the gas equals the work done by the gas : Q = W . Note from Eq. ( .
) that for V > V , W > ; and for V < V , W < . That is, in an isothermal expansion, the gas absorbs heat and does work while in an isothermal compression, work is done on the gas by the environment and heat is released. . .
Adiabatic process In an adiabatic process, the system is insulated from the surroundings and heat absorbed or released is zero. From Eq. ( . ), we see that work done by the gas results in decrease in its internal energy (and hence its temperature for an ideal gas).
We quote without proof (the result that you will learn in higher courses) that for an adiabatic process of an ideal gas. P V γ = const ( . ) where γ is the ratio of specific heats (ordinary or molar) at constant pressure and at constant volume. γ = Cp Cv Thus if an ideal gas undergoes a change in its state adiabatically from ( P , V ) to ( P , V ) : P V γ = P V ( .
) Figure11. shows the P - V