One mole of the hydrogen gas has a volume of 0.060m 3 is compressed adiabaticall

Question

One mole of the hydrogen gas has a volume of 0.060m3 is compressed adiabatically until its final volume ishalf of its original volume.The initial mean kinetic energy permolecule of the gas is
1.38 x 10-20 J. Calculate (a) the initial pressure (b) the final pressure of the gas. Assume the hydrogen gas bahaves as an idealdiatomic gas. One mole of the hydrogen gas has a volume of 0.060m3 is compressed adiabatically until its final volume ishalf of its original volume.The initial mean kinetic energy permolecule of the gas is
1.38 x 10-20 J. Calculate (a) the initial pressure (b) the final pressure of the gas. Assume the hydrogen gas bahaves as an idealdiatomic gas.

Explanation / Answer

Initial volume of Hydrogen V = 0.060m3 The initial mean kinetic energy per molecule of the gas K.E = 1.38 x 10-20 J                                                                        (3 / 2 ) k T = 1.38 x 10-20 J where k = Boltzmann constant = 1.38 * 10 -23J / K So, Initial temperature of the hydrogen gas T = ( 2 / 3) [ ( 1.38 x 10-20 J ) / ( 1.38 x 10-23 J / K)                                                                     = 666.66 K (a). From gas equation PV = nRT Initial pressure P = nRT / V where R = Gas constant = 8.314 J / mol K            n= No.of moles = 1     P = 92377.77 Pa (b). Given final volume V ' = V / 2 In adiabatic process P V = P ' V ' where = Ratio of specific heats = 1.4 where = Ratio of specific heats = 1.4 Final pressure P ' = P [ V / V ' ]                               = 2.639 P                               = 243786.4 Pa                               = 2.639 P                               = 243786.4 Pa                                

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