Question

Gas at ${27}^{\circ }C$ temperature and 30 atmospheric pressure is allowed to expands to the spherical pressure. If the volume becomes 10 times its initial volume then the final temperature becomes.

• A. ${173}^{\circ }K$
• B. ${173}^{\circ }C$
• C. $-{173}^{\circ }C$
• D. $-{173}^{\circ }K$

Answer 1

The correct option is C $-{173}^{\circ }C$

Given that,

Pressure $P^{\prime }=30atm$

Volume $V^{\prime }=V$

Temperature $T^{\prime }=27+273-{300}^{0}k$

Pressure $P^{\prime \prime }=1atm$

Volume $V^{\prime \prime }=10V$

We know that,

$\frac{P^{\prime }{V}^{\prime }}{T^{\prime }}=\frac{P^{\prime \prime }{V}^{\prime \prime }}{T^{\prime \prime }}$

$\frac{30V}{300}=\frac{1\times 10V}{T^{\prime \prime }}$

$T^{\prime \prime }=\frac{300\times 10V}{30V}$

$T^{\prime \prime }=100K$

Now the temperature in Celsius

$T^{\prime \prime }=100-273$

$T^{\prime \prime }=-{173}^{0}C$

Hence, the final temperature is $-{173}^{0}C$