Relation between change of pressure and temperature in adiabatic process

T C · Sep 13, 2023

In case of adiabatic process, we all know that the relation between temperature and pressure and that's given below:

P. T^(γ/(1-γ)) = Const.
therefore, P = Const. T^{(γ/(γ - 1))}
or, ΔP = Const. (γ/(γ - 1)).ΔT^{(1/(γ - 1))}

It's just an attempt to find out the relation. Don't know how much correct I am. Waiting for comments from others.

jack action · Sep 13, 2023

No, it is:
$$P_0T_0^k = C$$
and:
$$PT^k = C$$
Therefore
$$P_0T_0^k = PT^k$$
Where ##k = \frac{\lambda}{1-\lambda}##. Thus:
$$\Delta P = P- P_0$$
$$\Delta P= P_0\left(\left(\frac{T_0}{T}\right)^k-1\right)$$
$$\Delta P = P_0\left(\left(\frac{T}{T_0}\right)^{-k}-1\right)$$
$$\frac{\Delta P}{P_0} = \left(\frac{T_0 + \Delta T}{T_0}\right)^{-k}-1$$
Or:
$$1+ \frac{\Delta P}{P_0} = \left(1+\frac{\Delta T}{T_0}\right)^{\frac{\lambda}{\lambda - 1}}$$

Relation between change of pressure and temperature in adiabatic process

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