First slide

Thermodynamic properties

Question

For a gas having molar mass M, specific heat at constant pressure can be given as:

Moderate

A

$\frac{{\gamma R}}{{M(\gamma - 1)}}\$
B

$\frac{\gamma }{{RM}}\$
C

$\frac{M}{{R(\gamma - 1)}}\$
D

$\frac{{\gamma RM}}{{\gamma + 1}}\$

Solution

$\frac{{{C_p}}}{{{C_v}}}\; = \;\gamma \$ ; $\frac{{{C_p}\; - \;{C_V}}}{{{C_v}}}\; = \;\gamma - 1\$
C_p= $\gamma$ C_v
C_p = Specific heat capacity at constant pressure
C_v = Specific heat capacity at constant volume
C_p - C_v =R
C_p x M - C_Vx M = R
${C_p} - \;{C_v} = \frac{R}{M}$
${C_p}\; = \;\frac{R}{M}\; + \;{C_v}\; = \;\frac{R}{M}\; + \;\frac{{{C_p}}}{\gamma }$
${C_p}\left[ {1\; - \frac{1}{\gamma }} \right]\;\; = \;\frac{R}{M}\$
${C_p}\; = \;\frac{R}{M}\; \times \;\frac{\gamma }{{\gamma \; - 1}}$
${C_p}\; = \;\frac{{\gamma R}}{{M(\gamma \; - 1)}}\$

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