Adiabatic relations for ideal gas with specific heat ratio

[ChronicQuantumAddict]

Ok, the first question is this:

It asks me to show that the following relation holds for a reversibe adiabatic expansion of an ideal gas:

T/P ^(1 - (1/Gamma)) = constant​

Where Gamma = the ratio of: C_p/C_v the specific heats with constant pressure and volume, respectively.

I know that PV ^Gamma = constant and that TV ^(Gamma - 1) = constant.
i just don't see the connection.

Second question:

An ideal gas undergoes an adiabatic reversible expansion from an initial state (T1, v1) to a final state (T2,v2).

Show:

ln (T_2/T_1) = (Gamma - 1) ln (v_1/v_2)​

again where Gamma = the ration of specific heats.

Please help, thanks

 

[Andrew Mason]

Ok, the first question is this:

It asks me to show that the following relation holds for a reversibe adiabatic expansion of an ideal gas:

T/P ^(1 - (1/Gamma)) = constant​

Where Gamma = the ratio of: C_p/C_v the specific heats with constant pressure and volume, respectively.

I know that PV ^Gamma = constant and that TV ^(Gamma - 1) = constant.
i just don't see the connection.

Express V in terms of P in the last equation:

$$V = kP^{-\frac{1}{\gamma}}$$

Second question:

An ideal gas undergoes an adiabatic reversible expansion from an initial state (T1, v1) to a final state (T2,v2).

Show:

ln (T_2/T_1) = (Gamma - 1) ln (v_1/v_2)​

again where Gamma = the ration of specific heats.

This can be written:

$$\frac{T_2}{T_1} = (\frac{V_1}{V_2})^{\gamma -1}$$

$$T_2V_2^{\gamma -1} = T_1V_1^{\gamma -1}$$

AM

 

[ChronicQuantumAddict]

thanks

thank u, this is really helping me for the test i have on wed next week, appreciated. glad i found this site