Question

please show me a sep wise solution for these problem as i am trying to learn from your solution. if you cant or you answer partially dont answer please.

Problem 3 (20 pts): Consider a Carnot engine cycle in which we take an ideal monoatomic gas from point Ou a)on first leg ofthe cycle, a-+ b, we take the gas through an isothermal expansion at temperature TH Given the values shown on the P and V axes for the state of the gas, what is V? 0.25 atm -0.3 b) On the first leg of the cycle, a-b, what is Q expressed in units of atm-L c) On the second leg of the cycle, b-c, we take the gas through an adiabatic expansion. Given the values shown in the diagram above, what is V.?

Answer 1

For isothermal expansion a rightarrow b P_a V_a = P_b V_b V_b = P_aV_a/P_a OR V_b = 2 times 1.01325 times 10^5 times 0.1 times 10^-3m^3/1 times 1.01325 times 10^5 = 0.2 times 10^-3m^3 = 0.2 Liter Q_H = W_a rightarrow b = nrT_H ln (V_b/V_a) but n = numberal males = P_aV_a/RT_H Q_H = P_aV_a/RT_H times RT_H ln (0.2/0.1) = 0.2 atm L times 0.6931 = 0.13862 atm - L Q_H = 0.13862 atm-L For expansion from b rightarrow c P_b V_b^r = P_c V_c^r [r = 5/3 for monoatomic gas] 1atm times (0.2)^5/3 = (0.25 atm) times V_c^5/3 V_c = 0.2 times (1/0.25)^3/5 = 0.2 times (4)^0.6 = 0.2 times 2.2974 = 0.4595 Litre V_C = 0.4595 Litre As dw = P dv for adiabatic Process from b rightarrow c P_bV_b^r = P_C V_c^r = k OR P V^r = k (In general) P = k/v^r Therefore dw = k/v^r dv and W_Total = integral_v_b^v_c k/V^r dv