We can define infinite number of specific heat capacities between two temperatures(e.g $c_p ,c_v$) . Could we do that for an adiabatic process. As for adiabatic process heat addition or removal is zero.
I asked this question because I found the work input equation for joule cycle defined for gas turbine unit and the equation is $$ c_p(T_2 - T_1)$$
How it is derived from STEADY FLOW ENERGY EQUATION. Work input is the work of compressor. Similarly we have turbine output equation as $$c_p(T_3 -T_4)$$
Where 1 to 2 is isentropic compression and 3 to 4 is isentropic expansion.