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Standard XII

Chemistry

Real Gases

The value of ...

Question

The value of $C_{p} - C_{v} = 1.00 R$ for a gas in state $A$ and $C_{p} - C_{v} = 1.06 R$ in another state. If $P_{A}$ and $P_{B}$ denote the pressure and $T_{A}$ and $T_{B}$ denote the temperatures in the two states, then

P_{A} = P_{B}

T_{A} > T_{B}

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P_{A} > P_{B}

T_{A} = T_{B}

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P_{A} < P_{B}

T_{A} > T_{B}

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P_{A} = P_{B}

T_{A} < T_{B}

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Solution

The correct option is C $P_{A} < P_{B}$ , $T_{A} > T_{B}$
Since we know that,
$C_{p} - C_{V} = n R$
Therefore, state A contain less number of moles of gas then state B
Hence, Pressure in state A will be less than Pressure in state B
whereas Temperature in state A will be greater than temperature in state B
Since,
$P \propto n$
$T \propto 1 / n$
Hence,
$P_{A} < P_{B}$
$T_{A} > T_{B}$
option (C)

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