How Do You Analyze a PV Diagram for a Diatomic Ideal Gas Cycle?

[joemama69]

Homework Statement

A diatomic ideal gas originally at pressure Po and volume Vo is heated at
constant volume until its pressure increases by a factor of 3. Next it is
isothermally expanded until its pressure returns to Po. Finally it is
isobarically compressed to its initial volume.

a) Show the process on a PV diagram.

b) Find Q, W, and delta E for each of the 3 legs [All entries should be in terms of the “givens”—
Po and Vo.]

Homework Equations

The Attempt at a Solution

Part A) Note the very crude attachment.

Part B) I think i have this generaly correct, but I am having trouble using the given terms

Leg 1 (AB)

Q = E = nC_v(delta T), W = 0

Leg 2 (BC)

Q = W, E = 0

Leg 3 (CA)

Q = E + W, W = P(delta V)

 

[ideasrule]

Q = E = nC_v(delta T), W = 0

That's right. Just express n, Cv, and delta-T in terms of gamma, P0, and V0. Remember that PV=nRT.

Leg 2 (BC)

Q = W, E = 0

Do you know how to find the work done by an isothermal process?

Leg 3 (CA)

Q = E + W, W = P(delta V)

Yeah. Now express delta-V in terms of V0.

 

[joemama69]

"That's right. Just express n, Cv, and delta-T in terms of gamma, P0, and V0. Remember that PV=nRT."

but PV isn't constant, how can is use the pv equation

 

[ideasrule]

PV isn't constant, but P1V1-P0V0 = nR(T1-T0).

 

[joemama69]

ok so i just solve that equatio for n and delta-T and plug those in...

n = (PV - initial PV)/R(detaT)... delta T = (PV-initial PV)/nR...

C_v is constand volume so is that just C_v = V_o

 

[joemama69]

leg 2...


Q = W = nRT(ln V/V_o), E = 0

leg 3...

Q = E + W, W = P(delta V) = P(v-v_o), can E be expressed in P & V