Question

Part A ConstantsI Periodic Table An ideal gas with γ = 1.4 occupies 6.0 L at 300 K and 150 kPa pressure and is compressed adiabatically until its volume is 2.0 L. It's then cooled at constant pressure until it reaches 300 K, then allowed to expand isothermally back to state A. Find the net work done on the gas Express your answer using two significant figures. 0図? W- Submit Request Answer Part B Find the minimum volume reached Express your answer using two significant figures. 0図? Vmin Submit Request Answer

Answer 1

r = 1.4, PV^r = constant (adiabatic eq), PV = RT (n = 1) for ideal gas v_1 = 6.0 L v_2 = 2.0 L T_1 = 300 k T_2 = ? implies T_2 = T_1 (P_2/P_1)^r - 1/r = T_1(v_1/v_2)^r - 1 P_1 = 150000 P_A P_2 = P_1(v_1/V_2)^r Total Work done, w = W_ad + W_isobaric + W_isothermal = P_1 v_1^r v^1 - r_2 - v^1 - r_1/1 - r + (-R)(300 - T_2) + (-R)300 ln V_d/v_i W_ad = 15 times 10^4 times 6^1.4(2^-0.4 - 6^-0.4)/(-0.4) tildeequal -12.42 J W_isobaric = -8.314 times (300 - 300(6/2)^0.4) tildeequal 1376.41 J using PV = RT, P_1V_1/T_1 = P_2V_2/T_2 (During isobaric process) implies P_1 = P_2 = P, T_1 = 300 times 3^0.4, T_2 = 300 v_1 = 2.01, V_2 = ? V-2 = V_1 T_2/T_1 = 2 times 1/3^0.4 L. So, V_2 = V_1 = 2/3^0.4 L (for isothermal process) Since, Finally we me returning to state A (initial state)