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Q.

10 litres of a monatomic gas at 0° C and 10 atm pressure is suddenly released to 1 atm pressure and the gas expands adiabatically against this constant pressure. The final temperature and volume of the gas respective! are :

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a

$T = 165.4 K, V = 78.8$ liters

b

$T = 161.2 K, V = 68.3$ liters

c

$T = 174.7 K, V = 64.00$ liters

d

$T = 153 K, V = 57$ liters

answer is A.

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Detailed Solution

$\begin{array}{l} n \times \frac{3}{2} R_{X} (T - 273) = - 1 (\frac{n \times R \times T}{1} - \frac{n \times R \times 273}{10}) \\ 1.5 T - 1.5 \times 273 = - T + 27.3 \\ 2.5 T = 16 \times 27.3 \\ T = 174.7 K \end{array}$

$\begin{array}{l} \frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}} \\ \Rightarrow V_{2} = \frac{10 \times 10}{273} \times \frac{174.7}{1} = 64 L \end{array}$

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