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  • Consider two containers A and B containing identical gases at the same pressure, volume and temperature.

Consider two containers A and B containing identical gases at the same pressure, volume and temperature. The gas in container A is compressed to half of its original volume isothermally while the gas in container B is compressed to half of its original value adiabatically. The ratio of final pressure of gas in B to that of gas in A is

a) 2^{\gamma-1}

b) \left (\frac{1}{2} \right )^{\gamma-1}

c) \left (\frac{1}{1-\gamma} \right )^{2}

d) \left (\frac{1}{\gamma-1} \right )^{2}

 

Answers (1)

The answer is the option (a). Let us consider a P-V diagram for container A and B. Compression of gas is involved in both the cases. For the isothermal process (gas A) during 1\rightarrow 2

P_1V_1=P_{2}V_{2}

P_{0}(2V_{0})=P_{2}V_{0}

 P_{2}=2P_{0}

For adiabatic process  1\rightarrow 2

P_{1}V_{1}^{\gamma }=P_2V_{2}^{\gamma}

P_{0}(2V_{0})^{\gamma }=P_{2}(V_{0})^{\gamma }

P_{2}=\left (\frac{2V_{0}}{V_{0}} \right )^{\gamma} P_{0}=2^{\gamma } P_{0}

\frac{(P_{2})_{B}}{(P_{1})_{A}}=\frac{2^{\gamma } P_{0}}{2P_{0}}=2^{\gamma -1}

Posted by

infoexpert24

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