Compressor work and Thermodynamics

[rishi kush]

how can we use Cp.dT to evaluate compressor work even when one side (inlet side) is having different pressure than other side (outlet side). Cp should be used for constant pressure!

 

[Chestermiller]

how can we use Cp.dT to evaluate compressor work even when one side (inlet side) is having different pressure than other side (outlet side). Cp should be used for constant pressure!

For a constant pressure process, the amount of heat Q is equal to $C_p\Delta T$. Otherwise, Q is not equal to that. But, for an ideal gas, irrespective of the pressure variation, the enthalpy change $\Delta H$ is always equal to $C_p\Delta T$. This is because, in thermodynamics, $C_p$ is defined in terms of the enthalpy change rather than in terms of the amount of heat transferred. The two definitions match only if the pressure is constant.

 

[rishi kush]

since Cp is a state function , its value should be different for initial and final states of a process? and which value should we have to consider?

 

[Chestermiller]

since Cp is a state function , its value should be different for initial and final states of a process? and which value should we have to consider?

If you have a heat capacity which varies with temperature, you integrate $dH=C_pdT$ between the initial and final temperatures to get the enthalpy change.