An idela with 7 degrees of freedom begins at a pressure of 8.5 atm, temperature

Question

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

A. How many moles of gas are there?

B.The gas expands isoberically to 200L

C. How much work was done in the expansion?

D.How much did the internal energy increase

E.What amount of heat flowed into the gas?

F. The gas then depressurizes isochorically to the orginal temperture. How much heat flowed out of the gas?

G.The gas contract isothermally back to the orignal volume. what would the sketch of thermal cycle look like in a PV diagram

H.How much work was done by the gas in the process?

I.how much flowed out in the system?

J.what is efficiency of the termal cycle?

K. what is the carnot effcieny for an ideal heat engine running between the same high nd low operating tempertures?

Explanation / Answer

P1 = pressure = 8.5 x 1.01 x 105 Pa

V1 = Volume = 120 L = 0.12 m3

T1= temperature = 25 c = 25 + 273 = 298 K

n = number of moles

Using the equation

P1V1 = nRT1

(8.5 x 1.01 x 105 ) (0.12) = n (8.314) (298)

n = 41.6

b)

V2 = 200 L = 0.2 m3

work done = P1 (V2 - V1) = (8.5 x 1.01 x 105 ) (0.2 - 0.12) = 68680 J

c)

at constant pressure

V1/T1 = V2 /T2

0.12 /298 = 0.20 / T2

T2 = 496.7 K

U = nCv (T2 - T1)

for degree of freedon = 7

Cv = 3.5 R

U = (41.6) (3.5 x 8.314) (496.7 - 298) = 240530 J

d)

Q = W + U = 68680 + 240530 = 309210 J

E)

T3 = 298 K

P3 = ?

Using P3 /T3 = P2 /T2

P3 /298 = ( 8.5 x 1.01 x 105 ) /496.7

P3 = 5.15 x 105 Pa

W = 0

U = nCv (T3 - T2)

for degree of freedon = 7

Cv = 3.5 R

U = (41.6) (3.5 x 8.314) (298 - 496.7) = - 240530 J

Q = - 240530 J

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