The figure above shows the path in the P-V plane that is followed by a reversibl

Question

The figure above shows the path in the P-V plane that is followed by a reversible Carnot engine that uses monatomic Argon gas as its working substance and operates by taking heat Qh = 3.3 kJ from a hot reservoir at Th = 1050 oC to do work and deposits waste energy Qc into a cold reservoir at Tc = 28 oC. At A, the Argon gas has a total internal energy of 17 kJ. What is is its internal energy at B?

What is the efficiency of this engine?

How much energy is deposited per cycle into the cold reservoir?

How many moles of Argon gas does the Carnot engine contain?

If the gas occupies a volume of 0.0025 m3 at point A, what it is the pressure at that point?

Extra credit: What is the value for the area bounded by this thermal cycle on the p-V diagram?

Explanation / Answer

a)

first

delta V = 0 if T = Th

therefore Ub = Ua = 17 kJ

b)

here

Q = 1 - Tc / Th

Q = 1 - (301 / 1323)

Q = 0.772

the efficiency of this engine is 0.772

c)

1 - Qc/Qh = 1 - Tc/Th = 0.772

Qc/Qh = 0.2275

Qc = Qh * 0.2275

Qc = 3.3 * 0.2275 = 0.75 kJ

the energy deposited per cycle into the cold reservoir is 0.75 kJ

d)

internal energy = 3 * n * R * T / 2 for monoatomic gas

3 * n * R *T / 2 = 17 * 10^3

n = 16 * 10^3 / ( 1.5 * 8.31 * 1323)

n = 0.97

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