An ideal gas with 7 degrees of freedom begins at a pressure of 8.5 atm, temperat

ID: 1486370 • Letter: A

Question

An ideal gas with 7 degrees of freedom begins at a pressure of 8.5 atm, temperature of 25 degrees celsius and volume of 120 L.

A) How many moles of gas are there?

B) The gas expands isobarically to 200 L. What is the new temperature?

C) How much work was done in the expansion?

D) By how much did the internal energy increase?

E) What amount of heat flowed into the gas?

F) The gas then depressurizes isochorically to the original temperature. How much heat flowed out of the gas?

G) Finally the gas contracts isothermally back to its original volume. Sketch this thermal cycle on a PV diagram.

H) How much work was done on the gas in the contraction?

I) How much heat flowed out of the system ?

J) What is the efficiency of this thermal cycle?

K) What is the carnot efficiency for an ideal heat engine running between the same high and low operating temperatures?

A) PV = nRT

=> n = PV/RT = 8.5 * 120 / [0.082 * (273 + 25)] = 41.74 moles

B) V1/T1 = V2/T2

=> T2 = T1V2/V1 = 298 * 200 / 120 = 496.7 K

C) Work done by gas, W = P(V2 - V1) = (8.5 * 101325) * (200 - 120) * 10-3 = 68.9 kJ

D) U = (f/2)nRT = (7 / 2) * 41.74 * 8.314 * (496.7 - 298) = 241.3 kJ

E) Heat flow into the gas, Q = U + Wgas = 241.3 + 68.9 = 310.2 kJ

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