Question

A gas at 10C temperature and $1.013\times {10}^5$ Pa pressure is compressed adiabatically to half of its volume. If the ratio of specific heats of the gas is 1.4, what is its final temperature?

• A. ${100}^{o}C$
• B. ${123}^{o}C$
• C. ${93}^{o}C$
• D. ${146}^{o}C$

Answer 1

The correct option is

A

${100}^{o}C$

$\text{Given:-}$Temperature, $T_1={10}^{\circ }C$

Pressure $=1.013\times {10}^5$

Ratio of specific heats $=1.4$

$\text{Solution:-}$

For Adiabatic process :-

$P{V}^{\gamma }=constant$

$T{V}^{\gamma -1}=constant$

$\Rightarrow T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$

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

$=(10+273){\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$

$=\left(283\right){\left(2\right)}^{1.4-1}$

$=283\times 2^{0.4}$

$=283\times 1.32$

$T_2=373.56K$ $or$

$T_2=373.56-273$

$T_2={100.56}^{\circ }C\approx {100}^{\circ }C$

$\text{Hence the correct option is A}$