版权所有：华东理工大学物理化学教研室 11 For a closed system of constant composition, U is a func-tion of V and T. When V changes to V + dV at constant T, U changes to U U ( U V ) V T ' = + ∂ ∂ d 2). Changes in internal energy U U ( U T ) T V ' = + ∂ ∂ d U U ( U V ) V ( U T ) T T V ' = + ∂ ∂ d + ∂ ∂ d U ( U V ) V ( U T ) T T V d = ∂ ∂ d + ∂ ∂ d When T changes to T+dT at constant V, U changes to 3.1 State functions
版权所有：华东理工大学物理化学教研室 11 For a closed system of constant composition, U is a func-tion of V and T. When V changes to V + dV at constant T, U changes to U U ( U V ) V T ' = + ∂ ∂ d 2). Changes in internal energy U U ( U T ) T V ' = + ∂ ∂ d U U ( U V ) V ( U T ) T T V ' = + ∂ ∂ d + ∂ ∂ d U ( U V ) V ( U T ) T T V d = ∂ ∂ d + ∂ ∂ d When T changes to T+dT at constant V, U changes to 3.1 State functions
版权所有：华东理工大学物理化学教研室 12 , the internal pressure, the same dimension as p T T V U π ⎟⎠⎞ ⎜⎝⎛ ∂∂ = V C T V U U V T d ⎟ d + d ⎠⎞ ⎜⎝⎛ ∂∂ = T V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ the slope of a plot of U against T at constant V. dU = πT dV + CV dT U ( U V ) V ( U T ) T T V d = ∂ ∂ d + ∂ ∂ d CV In a closed system of constant composition, dU is proportional to dV and dT, the coefficients of proportionality being the partial derivatives. 3.1 State functions
版权所有：华东理工大学物理化学教研室 12 , the internal pressure, the same dimension as p T T V U π ⎟⎠⎞ ⎜⎝⎛ ∂∂ = V C T V U U V T d ⎟ d + d ⎠⎞ ⎜⎝⎛ ∂∂ = T V U ⎟⎠⎞ ⎜⎝⎛ ∂∂ the slope of a plot of U against T at constant V. dU = πT dV + CV dT U ( U V ) V ( U T ) T T V d = ∂ ∂ d + ∂ ∂ d CV In a closed system of constant composition, dU is proportional to dV and dT, the coefficients of proportionality being the partial derivatives. 3.1 State functions