Question

A gas is suddenly compressed to $\frac{1}{4}$ th of its original volume. What is the rise in the temperature, the original temperature being ${27}^{0}C$ and y = 1.5?

• A. 327${}^{0}C$
• B. 350${}^{0}C$
• C. 400${}^{0}C$
• D. 450${}^{0}C$

Answer 1

The correct option is A 327${}^{0}C$

Since, the gas has been suddenly compressed it means the process is adiabatic. So, for an adiabatic process:

$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}......\left(1\right)$

Where, $T_1$is initial temperature, $T_1=300K$

$T_2$is final temperature

$V_1$is initial volume

$V_2$is final volume

$\gamma =1.5$

Since it is given that,

$V_2=\frac{V_1}{4}$

Using all values in equation (1)

$300{\left(V_1\right)}^{1.5-1}=T_2{\left(\frac{V_1}{4}\right)}^{1.5-1}$

$300{\left(V_1\right)}^{0.5}=T_2\frac{{\left(V_1\right)}^{0.5}}{{\left(4\right)}^{0.5}}$

$300=\frac{T_2}{2}$

$T_2=600K$

$T_2=327{}^{0}C$