An ideal gas with 5 degrees of freedom begins at a pressure of 7.5 atm, temperat

Question

An ideal gas with 5 degrees of freedom begins at a pressure of 7.5 atm, temperature of 25 C and a volume of 120L.

A) How many moles of gas are there?

B) The gas expands isobarically to 240L. 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. Indicate pressure and volume values on each axis for the beginning/ end of each process.

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?

kK) What is the Carnot efficiency for an ideal heat engine running between the same high and low temperatures? Thank you in advance! Please list all the steps.

Explanation / Answer

(a)
Pressure = 7.5 atm
Pressure = 7.5 * 101325 Pa = 7.6 * 10^5 Pa
Volume = 120 L = 0.12 m^3
T = 25 C = 298 K

For an Ideal Gas -
pv = nRT
7.6 * 10^5 * 0.12 = n*8.314 * 298
n = 36.81 moles
No of moles of a Gas, n = 36.81 moles

(b)
Isobaric Process is a Process in which Pressure remains constant.
New Volume = 240 L = 0.240 m^3
pv = nRT
7.6 * 10^5 * 0.24 = 36.81 * 8.314 * T
T = 596 K
New Temperature, T = 596 K

(C)
Work done by Gas in Isobaric Process is given by,
W = P * V
W = 7.6 * 10^5 * (Vf - Vi)
W = 7.6 * 10^5 * (0.24 - 0.12)
W = 91200 J = 91.2 KJ
Work done in the Expansion, W = 91.2 KJ

(D)
U = n Cv T

Cv = 5/2 * R
U = 36.81* 5/2 * 8.314 * (596 - 298)
U = 228 KJ

Change in Internal Energy, U = 228 KJ

E)
We know,
Q = U + W
Q = 228 KJ + 91.2 KJ
Q = 319.2 KJ

Heat Floweed into the Gas, Q = 319.2 KJ

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.