Energy and Entropy from P-V Diagram

In summary: What is the change in entropy per mole of gas in going from b to c? ΔSbc = J/K Use: dS = dQ/T. What is the heat flow in terms of dT and Cv? Integrate that to get ΔS. There is a change in entropy of 0.27 j/K when going from b to c.
  • #1
Rapier
87
0

Homework Statement


An ideal monatomic gas is taken through the above cycle where p1= 2 X 105 Pa and V1 = 5 cm3. During the cycle both the pressure and volume will change such that p2 = 2 p1 and V2 = 4 V1.

a) How much work is done by the gas in going from state a to state c along path abc?
Wabc = 3 J
OK

b) What is the change in internal energy in going from b to c?
Ubc= J

c) What is the change in internal energy during the complete cycle?
UTOT = 0 J
OK

d) What is the change in entropy per mole of gas in going from b to c?
ΔSbc = J/K

e) What is the change in entropy per mole during the complete cycle?
ΔSTOT= 0 J/K
OK

I am having problems with Parts B and D.

Homework Equations


PV=NRT
Q = nCvdt


The Attempt at a Solution



I only have P and V. I cannot use the Ideal Gas Law to calculate n or T because I have two unknowns. I cannot use my Heat Equations because I am still missing n and T. I'm just stuck. If I can calculate B, I think I can get D...I just don't see any way to calculate the Heat in part B. HELP!

Thanks.
 

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  • #2
Rapier said:
b) What is the change in internal energy in going from b to c?
Ubc= J
Use: ΔU = nCvΔT = n(3R/2)ΔT

Since PV = nRT, you can express ΔT in terms of ΔP and V (V is constant).

d) What is the change in entropy per mole of gas in going from b to c?
ΔSbc = J/K
Use: dS = dQ/T. What is the heat flow in terms of dT and Cv? Integrate that to get ΔS.

AM
 
  • #3
Andrew Mason said:
Use: ΔU = nCvΔT = n(3R/2)ΔT

Since PV = nRT, you can express ΔT in terms of ΔP and V (V is constant).

Use: dS = dQ/T. What is the heat flow in terms of dT and Cv? Integrate that to get ΔS.

I can't believe I didn't see that. Once I read "express ΔT in terms of ΔP and V" it all fell together. It took me less than 2 minutes to solve the problems. Thanks! :)
 

FAQ: Energy and Entropy from P-V Diagram

What is energy and entropy?

Energy is the ability to do work or cause change. It exists in many forms, such as thermal, electrical, and chemical. Entropy is a measure of the disorder or randomness in a system. In simple terms, it describes the tendency of systems to move towards a more disordered state.

What is a P-V diagram?

A P-V (pressure-volume) diagram is a graphical representation of the relationship between pressure and volume in a thermodynamic system. It is often used to visualize the work done by a system as it undergoes a change in volume.

How is energy and entropy related in a P-V diagram?

In a P-V diagram, the area under the curve represents the work done by the system. The steeper the curve, the more work is done and the more energy is transferred. Entropy, on the other hand, is related to the amount of heat transferred into or out of the system. A larger area under the curve indicates a larger change in entropy.

What does a horizontal line on a P-V diagram represent?

A horizontal line on a P-V diagram represents an isothermal process, where the temperature remains constant. This means that the system is exchanging heat with its surroundings, but there is no change in internal energy. The entropy of the system remains constant during an isothermal process.

What does a vertical line on a P-V diagram represent?

A vertical line on a P-V diagram represents an isobaric process, where the pressure remains constant. This means that the system is exchanging energy with its surroundings, but there is no change in volume. The energy transferred during an isobaric process contributes to the change in entropy of the system.

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