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Three step gas cycle 
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#1
Feb2710, 09:35 PM

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 threestep 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_1T_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 rearranged 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 ? 


#2
Feb2710, 10:18 PM

P: 1,133




#3
Feb2710, 10:40 PM

P: 12

But i still dont know how to figure this problem out! please help anyone!!!! pleaseeeeeeeeee!!! 


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