The discussion focuses on evaluating compressor work using the heat capacity at constant pressure, denoted as Cp, despite pressure variations between the inlet and outlet sides. It is established that for an ideal gas, the enthalpy change (ΔH) can be calculated using the formula ΔH = CpΔT, which holds true regardless of pressure differences. The conversation emphasizes that Cp is a state function, and its value may differ between initial and final states, necessitating integration of dH = CpdT when heat capacity varies with temperature.
PREREQUISITESEngineers, thermodynamics students, and professionals involved in compressor design and analysis will benefit from this discussion, particularly those seeking to understand the relationship between heat capacity and compressor work in varying pressure conditions.
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 said: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!
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.rishi kush said: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?