Thermodynamics work done calculation using specific heat capacity?

by

Hi can someone please explain why it is possible to use the equation w = Cp(delta T) for processes where pressure doesn’t remain constant? For example, in the Brayton cycle the specific work gained by the turbine via expansion can be calculated using w = Cp(T3-T4′) but during the expansion the pressure changes so why is it ok to use the ‘specific heat at constant pressure’ constant,? Thank you very much!

✅ Answers

? Best Answer

  • A turbine is an open thermodynamic system. Assuming it to be in a steady state, we get:
    Q – W = m ( h_e – h_i + (V_e^2 – V_i^2)/2 + g(z_e – z_i) )

    For a turbine,we generally have Q = 0 (well insulated, no heat gain/loss), and the second and third terms on the RHS (representing changes in kinetic energy and gravitational potential energy) are negligible. Hence, we have:

    W = m (h_i – h_e)

    Now, if we have the fluid to be an ideal gas with constant specific heats, then we get:

    W = m Cp (T_i – T_e)

    Hope this helps.

    • Leave a Comment