ALphysics question about gases

Atheist

2010-11-30 3:53 am

A and B are two identical containers connected by a tap S initially closed.
A contains an ideal gas at a pressure P1 and a temperature T1.
B contains the same gas at a pressure P2 and temperature T2.
The tap S is then opened.
If the temperatures of the containers A and B remain constant at T1 and T2 respectively, prove that the final pressure of the gas mixture is (P1T2+P2T1)/(T1+T2).

( You may refer to the HKALE 1985 physics MC question No.10. )

回答 (1)

天同

2010-11-30 4:16 am

✔ 最佳答案

Let n1 be the no. of moles of gas initially in container A, and n2 be the no. of moles of gas initially in container B
Applying the Ideal Gas Equation: PV = nRT, we have,(P1).V = (n1).R(T1) and (P2).V = (n2).R(T2)
where V is the volume of each container
hence, (n1+n2) = (P1)V/R(T1) + (P2)V/R(T2)

After the gas is mixed, apply the Ideal Gas Equation again,
(n1' + n2') = PV/R(T1) + PV/R(T2)
where n1' and n2' are the new no. of moles of gas in conatiners A and B respectively.
P is the common final pressure

By conservation of mass, (n1 + n2) = (n1' + n2')
i.e. (P1)V/R(T1) + (P2)V/R(T2) = PV/R(T1) + PV/R(T2)
(P1)/(T1) + (P2)/(T2) = P(1/T1 + 1/T2)
after simplifying and solve for P, we could get,
P = [(P1).(T2) + (P2).(T1)]/(T1 + T2)

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