Thermal Physics> one mole of an ideal monatomic gas is cau...

one mole of an ideal monatomic gas is caused to go through the cycle shown in Fig. 24-22. (a) How much work is done on the gas in expanding the gas from a to c along path abc? (b) What is the change in internal energy and entropy in going from b to c? What is the change in internal energy and entropy in going through one complete cycle? Express all answer in terms of the pressure p₀ and volume V₀ at point a in the diagram.

Shane Macguire , 10 Years ago

Grade upto college level

2 Answers

Deepak Patra

Last Activity: 10 Years ago

Kushagra Madhukar

Dear student,

Please find the solution to your problem.

(a) W = – PΔV

= – p_o(4V_o – V_o) = – 3p_oV_o

So, W_abc = W_ab = – 3p_oV_o

Hence, work done on the gas in the path abc will be – 3p_oV_o

(b) The change in internal energy ΔE_bc along the path b to c would be,

ΔE_bc = 3/2nRΔTbc

= 3/2(nRT_c – nRT_b)

= 3/2(P_cV_c – PbV_b) [PV = nRT]

= 3/2[(2p_o)(4V_o) – (p_o)(4V_o)]

= 3/2 x 4p_oV_o

= 6p_oV_o

The change in entropy ΔS_bc along the path b to c would be

ΔS_bc = 3/2 nR ln(T_c/T_b)

= 3/2 nR ln(P_c/P_b) [since, V remains constant from b to c hence, T_c/T_b = P_c/P_b]

= 3/2 nR ln(2p_o/p_o)

= 3/2 nR ln2

Thanks and regards,

Kushagra

Last Activity: 5 Years ago

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Thermal Physics> one mole of an ideal monatomic gas is cau...

Shane Macguire , 10 Years ago

Deepak Patra

Kushagra Madhukar

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