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two containers of equal volume contain same gas at pressure P1 and P2 and absolute temperature T1 and T2 respectively. on joining the vessels, the gas reaches a commmon pressure P and common temperature T. the ratio of P/T is

two containers of equal volume contain same gas at pressure P1 and P2 and absolute temperature T1 and T2 respectively. on joining the vessels, the gas reaches a commmon pressure P and common temperature T. the ratio of P/T is

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

Let the volume of each container beV.

From ideal gas equation,

Number of moles of gas molecules in the containers is

n_1=\dfrac{P_1V}{RT_1}

n_2=\dfrac{P_2V}{RT_2}

Since the number of particles will remain the same,

Number of particles before joining=Number of particles after joining
\implies \dfrac{P_1V}{RT_1}+\dfrac{P_2V}{RT_2}=\dfrac{P(2V)}{RT}
\implies \dfrac{P}{T}=\dfrac{1}{2}(\dfrac{P_1}{T_1}+\dfrac{P_2}{T_2})

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