An inflated rubber balloon contains one mole of an ideal gas, has a pressure P, volume V and temperature T. If the temperature rises to $1.1$ T, and the volume is increased to $1.05$ V, the final pressure will be.

1.1

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Less than P

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Between P and

1.1

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Solution

The correct option is D Between P and $1.1$ P
Using $P V = n R T$ or $\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$
Here, $P_{1} = P$ , $V_{1} = V$ , $T_{1} = T$ , $T_{2} = 1.1$ T and $V_{2} = 1.05$ V
$∴ P_{2} = \frac{P_{1} V_{1} T_{2}}{V_{2} T_{1}} = \frac{P \times V \times 1.1 T}{1.05 V \times T} = 1.05$ P

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An insulated container of two diatomic gases has two chambers separated by an insulting partition. One of the chambers has volume $V_{1}$ and contains ideal gas at pressure $p_{1}$ and temperature $T_{1}$ . The other chamber has volume $V_{2}$ and contains ideal gas at pressure $p_{2}$ and temperature $T_{2}$ . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be