Question

Helium at $27^{\circ} C$ has a volume $8$ litres. It is suddenly compressed to a volume of $1$ litre. The temperature of the gas will be $(V=5 / 3)$

• A. $9327^{\circ} C$
• B. $ 1200^{\circ} C $
• C. $ 927^{\circ} C $
• D. $ 108^{\circ} C $

Answer 1

Answer: (C)

$T_{1} V_{1}^{\gamma-1} =T_{2} V_{2}^{\gamma-1} $
$T_{2} =\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1} T_{1} $
$ T_{2} =\left(\frac{V_{1}}{V_{2}}\right)^{\frac{5}{3}-1} \times 300 $
$T_{2} =\left(\frac{8}{1}\right)^{2 / 3} \times 300$
$=4 \times 300 $
$=1200 K =927^{\circ} C $