The figure shows a reversible cycle through which 1.71 mol of a monatomic ideal

Question

The figure shows a reversible cycle through which 1.71 mol of a monatomic ideal gas is taken. Assume that p = 2p_0, V = 2V_0, p_0 = 3.14 times 10^5 Pa, and V_0 = 0.0213 m^3. Calculate (a) the work done during the cycle, (b) the energy added as heat during stroke abc, and (c) the efficiency of the cycle, (d) What is the efficiency of a Carnot engine operating between the highest and lowest temperatures that occur in the cycle? (e) Is this greater than or less than the efficiency calculated in (c)?

Explanation / Answer

Given,
p = 2p0 ; V = 2V0 ; p0 = 3.14 x 10^5 Pa and V0 = 0.0213 m^3

A) The work done will be given by:

W = (p - p0)(V - V0)

W = p0 V0

W = 3.14 x 10^5 Pa x 0.0213 m^3 = 6.69 x 10^3 J

Hence, W = 6.69 x 10^3 J = 6.69 kJ

b)The energy added during abc, will be:

E = 3/2 p0 V0 + 5/2 x (2p0 V0)

E = 13/2 p0 V0

E = 13/2 x 3.14 x 10^5 Pa x 0.0213 m^3 = 4.35 x 10^3 J

Hence, E = 4.35 kJ

c)efficient will be:

e = 2/13 x 100 = 15.38 %

Hence, e = 15.38 %

d)for a carnot engine

e = [1 - Ta/Tc]x100

e = [1 - p0 V0/(2 p0 2V0)]x 100 = (1-1/4)x 100 = 75%

Hence, e = 75%

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