Question

9. 2.08/6.25 points | Previous Answers KatzPSE1 21.P044 In the figure below, an ideal gas undergoes a change in state from A to C by two different paths: ABC and AC. 8.00 Pa 4.00 Pa 0016.00 m3 (a) Along which path is the least amount of work done by the gas? ABC AC (b If the thermal energy of the gas at A IS 11 J and the heat transferred to the gas a on the path AC 210 נ find the thermal energy of the gas a Your response differs from the correct answer by more than 10%. Double check your calculations. J (c) If the thermal energy of the gas at state to change ts state from A วิ C Bis24 find the amount of heat added to the gas

Answer 1

Work done along the path ABC (W_ABC) = work done along AB + work done along BC = area under the line AB + area under the line BC = 0 + BC times BD {because Area under the line BC will be equal to area to area of rectangle BCED which is BC times BD} = 0 + (16 - 4) times 8 = 96 J work done along the path AC = area of trapezium ACED W_AC = 1/2 times (AD + EC) times DE = 1/2 times (4 + 8) times (16 - 4) = 72 J So least work will be done along AC. U_A = 11 J, Q_AC = 210 J, U_C = ? we know that work done along path AC - W_AC = 72 J By first law of thermodynamics for path AC - Q_AC = (U_C - U_A) + W_AC rightdoublearrow 210 = (U_C - 11) + 72 U_C = 210 + 11 - 72 U_C = 149 J