A heat engine does work by using a gas at an initial pressure of 1000 Pa and vol
ID: 1731972 • Letter: A
Question
A heat engine does work by using a gas at an initial pressure of 1000 Pa and volume .1m 3. Step-by-step, it then increases the pressure to 10,000 Pa (at constant volume), increases the volume to .15m3 (at constant pressure), decreases the pressure back to 1,000 Pa (at constant volume) and returns the volume back to .1m3 (at constant pressure).
8) What is the change in internal energy during the first step?
DU = 0 J
DU = 450 J
DU = 500 J
DU = 750 J
DU = 1250 J
DU = 1350 J
9) What is the change in internal energy during the second step?
DU = 0 J
DU = 450 J
DU = 500 J
DU = 750 J
DU = 1250 J
DU = 1350 J
11) How much heat is added to the gas in the first step?
Q = 0 J
Q = 450 J
Q = 500 J
Q = 750 J
Q = 1250 J
Q = 1350 J
12) How much heat is added to the gas in the second step?
Q = 0 J
Q = 450 J
Q = 500 J
Q = 750 J
Q = 1250 J
Q = 1350 J
13) How much heat is added to the gas in one complete cycle?
Q = 0 J
Q = 450 J
Q = 500 J
Q = 750 J
Q = 1250 J
Q = 1350 J
Explanation / Answer
given heat engine
Pi = 1000 Pa
Vi = 0.1 m^3
step 1, constant volume
P1 = 10,000 Pa
work done W1 = 0
now
PiVi = nRTi
P1Vi = nRT1
U1 = nCv(T1 - Ti) = Cv(P1 - Pi)Vi/R
for air, gamma = 1.4
Cp/Cv = 1.4
Cp - Cv = R
0.4Cv = R
Cv = 10R/4 = 5R/2
Cp/Cv = 1.4
Cp = 1.4*5*R/2 = 7R/2
8. U1 = 2.5(10,000 - 1000)*0.1 = 2250 J
9. step 2
constant pressure
V2 = 0.15 m^3
Work Done = P1(V2 - V1) = 500 J
Heat Supplied = nCp(T2 - T1) = 7(V2 - V1)P1/2 = 1750 J
hence change in internal energy = Q - W = 1250 J
11. heat added in first step = U1 = 2250 J
12. heat added in second step = 1750 J
13 constnat volume
P3 = 1,000 Pa
U3 = 2.5(1000 - 10000)*0.15 = -3375 J
heat added in third step = -3375 J
heat added in 4th step = 7(0.1 - 0.15)*1000/2 = -175J
total heat added = 450 J per cycle
d.
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