13_4: A flexible balloon contains 0.385 mol of an unknown polyatomic gas. Initia

Question

13_4: A flexible balloon contains 0.385 mol of an unknown polyatomic gas. Initially the balloon containing the gas has a volume of 7350 cm^3 and a temperature of 21.0 degree C. The gas first expands isobarically until the volume doubles. Then it expands adiabatically until the temperature returns to its initial value. Assume that the gas may be treated as an ideal gas with C(sub(p)) = 33.26J/mol*K and gamma = 4/3.
a. What is the total heat Q supplied to the gas in the process?
Q =?
b. What is the total change in the internal energy DeltaU of the gas?
DeltaU =?
c. What is the total work W done by the gas?
W =?
d. What is the final volume V?
V =?

Explanation / Answer

No.of moles n = 0.385 Initial volume V = 7350 cm^ 3 = 7350* 10 ^-6 m^ 3 initial temperature T = 21 oC = 21 + 273 = 294 K Initial pressure P = nRT / V    where R == gas constant = 8.314 J / nol K                            = 128.03* 10^ 3 Pa final volume V ' = 2V = 14700 * 10 ^-6 m^ 3 final temperature T ' = ( V ' / V ) T   Since pressure is constant                                 = 588 K Cp = 33.26 J / mol K = 4/ 3 In isobaric process : ------------------- heat Q = [n*Cp *(T'-T) ] = 3764.7 J work done W = P ( V ' - V )                        = 941 J Change in internal energy U = Q - W = 2823.7 J In adiabatic process : --------------------- heat Q ' = 0 work done W ' = [nR / (-1) ] [ T ' - T ]                         = 2823.7 J change in internal energy U ' = Q '-W ' = -2823.7 J (a). the total heat Q supplied to the gas in the process            Q " = Q + Q ' = 3764.7 J (b). the total change in the internal energy DeltaU of the gas U = U + U ' = 0 c. the total work W done by the gas W = W + W ' = 3764.7 J
d.the final volume V ' = 2V = 14700 * 10 ^-6 m^ 3

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