Three step gas cycle

by xmonsterx
Tags: cycle, step
 P: 12 1. The problem statement, all variables and given/known data A monatomic ideal gas has pressure p_1 and temperature T_1. It is contained in a cylinder of volume V_1 with a movable piston, so that it can do work on the outside world. Consider the following three-step transformation of the gas: 1. The gas is heated at constant volume until the pressure reaches Ap_1 (where A >1). 2. The gas is then expanded at constant temperature until the pressure returns to p_1. 3. The gas is then cooled at constant pressure until the volume has returned to V_1. It may be helpful to sketch this process on the pV plane. Part 1- How much heat DeltaQ_1 is added to the gas during step 1 of the process? Express the heat added in terms of p_1, V_1, and A. Part 2- How much work W_2 is done by the gas during step 2? Express the work done in terms of p_1, V_1, and A. Part 3- How much work W_3 is done by the gas during step 3? If you've drawn a graph of the process, you won't need to calculate an integral to answer this question. Express the work done in terms of p_1, V_1, and A. 2. Relevant equations R = 8.31 3. The attempt at a solution Part 1- I tried Q = p_1*V_1*(C_V/R) = 1.5*Ap_1*V_1 but I was told this is the final internal energy, not the change in internal energy. so I worked out that Q = [1.5*p_1*V_1*(AT_1-T_1)] / T_1 but the answer does not depend on AT_1 or T_1 Part 2- all I've got so far is W = nRT*ln(V_f/V_i) = pV*ln(V_f/V_i) but thats about as far as I get. Part 3- I got Ap_1*V_1 but this is what the value would be if it were coming from V = 0. So I re-arranged pV=nRT to eventually get W = p_1[(p_1V_1)/(Ap_1) - V_1] but this is also wrong how do I take into account the initial state, wouldn't I just be able to write W = (Ap_1V_1) - V_1 ?
P: 1,133
 Quote by xmonsterx Consider the following three-step transformation of the gas: 1. The gas is then expanded at constant temperature until the pressure returns to p_1. 2. The gas is then cooled at constant pressure until the volume has returned to V_1.
I think the first step isn't mentioned.
P: 12
 Quote by Gear300 I think the first step isn't mentioned.
thanks for point that out!! i fixed it!!! now its a three step cycle.

But i still dont know how to figure this problem out!