First slide

Heat ;work and internal energy

Question

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_{P}$ and $C_{V}$ respectively, if $δ = \frac{C_{p}}{C_{v}}$ and R is the universal gas constant, then $C_{V}$ is equal to?

Moderate

A

$\frac{R}{δ-1}$
B

$\frac{δ-1}{R}$
C

$δR$
D

$\frac{1+δ}{1-δ}$

Solution

We know that $C_{P} {-C}_{V} =R$ but
$δ= \frac{C_{P}}{C_{V}} {δC}_{V} {=C}_{p}$
substitute in above equation
${δC}_{V} {-C}_{V} =R \Rightarrow C_{V} [δ-1] =R \Rightarrow C_{V} = \frac{R}{δ-1}$

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