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Specific Heat Capacity

A certain amo...

Question

A certain amount of gas ( $P = 5 a t m, V = 2 L, T = 500 K$ ) in state $A$ is compressed to state $B$ ( $P = 2 a t m, T = 100 K, V = ?$ ). The final volume of gas in state $B$ in litre is:

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Solution

Assume the gas to be ideal.

For an ideal gas,

$P V = n R T$

Since the number of moles are constant,

$\frac{P V}{T} = constant$

During transformation,

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

$V_{2} = \frac{P_{1} V_{1} T_{2}}{P_{2} T_{1}} = \frac{5 \times 2 \times 100}{(2 \times 500)} = 1 L$

Hence, the correct answer is $1$ .

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