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A certain volume of dry air at 20 degree Celsius is expanded to three times of its initial volume 1)slowly 2) suddenly .calculate the final pressure and temperature in each case .Gamma of air =1.4

A certain volume of dry air at 20 degree Celsius is expanded to three times of its initial volume 1)slowly 2) suddenly .calculate the final pressure and temperature in each case .Gamma of air =1.4

Grade:12

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

When gas is expanded slowly, the pressure of the dry air remains the same throughout the process. Hence from ideal gas equation,V\propto T
Hence the temperature also becomes 3 times its inital value=3\times 293K=879K=606^{\circ}C

When the gas is suddely expanded, the process becomes an adiabatic one, and hence follows the relation,

PV^{\gamma}=constant
\implies \dfrac{P_2}{P_1}=\dfrac{1}{3}^{1.4}=3^{-1.4}

AlsoTV^{\gamma-1}=constant
\implies\dfrac{T_2}{T_1}=3^{-0.4}

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