Question

1 00 mol of a perfect gas initially at 1 00 atm and 298 K with Cpm (7/2) R is put through the following cycle () constant-volume heating to twice its initial temperature (u) reversible, adiabatic expansion back to its onginal temperature () reversible, isothermal compression back to 1 00 atm Calculate q, w, AU, and AH for each of the steps ()-(m) above Hints First calculate AU, then q AH easily follows Remember the meaning of an adiabatic process (u) (ut) Remember that the process is iISothermal and reversible (13)

Answer 1

Given that A sample of 1.00 mol a perfect gas initially at 1.00 atm and 298 the following cycle c pm = (1/2) R volume heating it initial temperature P_1 = 1 atm approx. 10^- 5 pa p_1 = n R P P_1 V_1 = nR p_1 n = 1 Rightarrow p_1 v_1 = RT_1 v_1 = RP_1/P_1 v_1 approx 0.025 m^3 reversible its original temperature T_2 = p_1 = 2 p_1 times 2.10^- 5 pa T_= 2 P v = constant T_2 = 596 adiabatic process T_f = p_i (v_i/v_f)^1/e where e = evm/R = epsilon m - R/R = 5/2 hence T_1 = T_2 (v_1/v_2)^/ or approx. m^3 thus we know T_1 = 298 p_2, P_2 = 596 p_2 p_1 = 10^- 5 pa, p_2 = 2 times 10^- 5 pa v_1 = 0.025 m^3 v_2 = 0.025 m^3