an ideal gas is taken through a series of thermodynamic processes as shown in th

Question

an ideal gas is taken through a series of thermodynamic processes as shown in the figure. Along the direct path a to c a total of 80 j of heat leaves the system, while 55 J of work is done on the system. In each of the following, give your answer in joules.

a) determine Ec - Et

b) on path cda 30 j work is done by the gas. How much heat is added to the gas in this process?

c) if Pa = 2.5 Pt0 how much work is done is done by the gas along path abc?

d) Along path abc what is Q?

e) If Ea -Eb = 10 j, what is Q along path bc?

Explanation / Answer

Q = delta E + W
heat input is +ve , Work done by gas is +ve , delta E is final E - initial E

a) there is no point 't'
I think it should be Ec - Ea
for direct process c-a, Q = -80, W = -55
-80 = (Ec-Ea) - 55
Ec - Ea = -25

b) Path cda, W = 30
Q = (Ea - Ec) + W = 25 + 30 = 55

c) Again Pa should be = 2.5 Pc or Pd
work done in constant pressure process = P ( change in volume)
W(ab) = - 2.5 W(cd) (-ve due to different sign of change in volume in two cases)
W(cda) = W(cd) , as W(da) = 0 (constant volume process w = 0
Wab = -2.5 W(cda) = -75 J = W(abc)

d) Q(abc) = Ec - Ea + W(abc) = -25 + (-75) = -100 j

e) Q(bc) = Ec - Eb + W(bc) = ( Ec- Ea) + ( Ea - Eb) + 0 = -25 + 10 = -15 j

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