# Specific heat capacity for Adiabatic process

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.

• Are you sure you have that straight? Those look to me like the heat flows during the constant pressure processes (since in such a process, the change in enthalpy, given by those expressions, is equal to the heat flow). Since the other processes are adiabatic, the sum of these two expressions will yield the total heat flow, and so the sum of these two expressions will also be the total work. – march Dec 30 '15 at 6:17
• @Sohail Ahmed what do you mean by infinite number of heat capacitites between two temperatures – 12sa Dec 30 '15 at 13:43
• Means e.g at constant pressure etc – Sohail Ahmed Dec 31 '15 at 2:50

Specific heat capacity is defined for a substance not for a process. Specific heat capacity depends on the structure of the substance but, it ($C_P$ for example) can be measured by the formula $$C_P=\left(\large{\frac {\partial h}{\partial T}}\right)_P=\left(\large{\frac {\partial q}{\partial T}}\right)_P$$

$C_P$ isn't a function of heat ($q$) or kind of process (isobaric, isochoric, isothermal, etc.)

As an obvious example, we can measure the volume of a container by measuring the volume of water that can fill it. But, all of us know that volume of a container depends on its dimensions not on volume of the water (If we don't have any water, doesn't container have a quantity called volume?!!:-)