<P> and for isothermal compressibility β T (\ displaystyle \ beta _ (T)): </P> <Dl> <Dd> β T = − 1 V (∂ V ∂ P) T = − 1 V (− V P) (\ displaystyle \ beta _ (T) = - (\ frac (1) (V)) \ left ((\ frac (\ partial V) (\ partial P)) \ right) _ (T) \ = - (\ frac (1) (V)) \ left (- (\ frac (V) (P)) \ right)) </Dd> </Dl> <Dd> β T = − 1 V (∂ V ∂ P) T = − 1 V (− V P) (\ displaystyle \ beta _ (T) = - (\ frac (1) (V)) \ left ((\ frac (\ partial V) (\ partial P)) \ right) _ (T) \ = - (\ frac (1) (V)) \ left (- (\ frac (V) (P)) \ right)) </Dd> <Dl> <Dd> β T = 1 / P (\ displaystyle \ beta _ (T) = 1 / P \,) </Dd> </Dl>

Explain relation between cp and cv of an ideal gas