Question

An ideal gas at ${27}^{o}C$ is compressed adiabatically to $\frac{8}{27}$ of its initial value. If $\gamma =\frac{5}{3}$, find the rise in temperature.

• A. ${275}^{o}C$
• B. ${375}^{o}C$
• C. ${400}^{o}C$
• D. ${300}^{o}C$

Answer 1

Answer: (B)

${375}^{o}C$

For an adiabatic process $T{V}^{\gamma -1}=constant$
For the states having temp and volume $(T_1,V_1)$ and $(T_2,V_2)$
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$ .....(1)
Given:
$V_2=\frac{8}{27}{V}_1$
$T_1={27}^{o}C=27+273=300K$
$\gamma =\frac{5}{3}$
Substituting the values in eqn(1)
$300\times V_1^{\frac{5}{3}-1}=T_2\times (\frac{8}{27}{V}_1{)}^{\frac{5}{3}-1}$
$\Rightarrow 300=T_2\times (\frac{2}{3}{)}^{3\times \frac{2}{3}}={675}^{o}K$
Rise in temperature = 675 - 300 = ${375}^{\circ }C$