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First law of thermodynamics, heat capacity

Problem 2.28

Two thermally insulated vessels 1 and 2 are filled with air and connected by a short tube equipped with a valve. The volumes of the vessels, the pressures and temperatures of air in them are known \(\left(V_{1}, p_{1}, T_{1}\right.\) and \(\left.V_{2}, p_{2}, T_{2}\right) .\) Find the air temperature and pressure established after the opening of the valve.

Reveal Answer
2.28.T=T122(p1V1+p2V2)/(p1V1T2+p2V2T1);p==(p1V1+p2V2)/(V1+V2).\begin{aligned} & 2.28 . T=T_{1}{ }_{2}^{2}\left(p_{1} V_{1}+p_{2} V_{2}\right) /\left(p_{1} V_{1} T_{2}+p_{2} V_{2} T_{1}\right) ; \quad p=\\ =&\left(p_{1} V_{1}+p_{2} V_{2}\right) /\left(V_{1}+V_{2}\right) . \end{aligned}
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