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The Ideal Gas Equation

The value of ...

Question

The value of $C_{p} - C_{v}$ is $1.09 R$ for a gas sample in state $A$ and is $1.00 R$ in state $B$ . Let $T_{A}, T_{B}$ denote the temperature and $P_{A}$ and $P_{B}$ denote the pressure of the states $A$ and $B$ respectively. Then:

A

P_{A} < P_{B}

and

T_{A} > T_{B}

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B

P_{A} > P_{B}

and

T_{A} > T_{B}

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C

P_{A} = P_{B}

and

T_{A} = T_{B}

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D

P_{A} > P_{B}

and

T_{A} < T_{B}

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Solution

The correct option is A $P_{A} < P_{B}$ and $T_{A} > T_{B}$
For state A, $C_{P} - C_{V} = R$ i.e. the gas behaves as ideal gas.
For state B, $C_{P} - C_{V} = 1.06 R (\neq R)$ i.e. the gas does not behave like ideal gas and we know that at high temperature & at low pressure the nature of gas may be ideal.
So, answer is option $A$ .

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