Solving Ideal Gas Problems: ΔE, ΔS, W & P0V0

[tigers4]

Homework Statement

1.0 mol of a monatomic ideal gas is taken through the cycle in the figure below.
http://s1142.photobucket.com/albums/n603/bdoneski/?action=view&current=20-26.gif"

a) What is the following as the gas goes from state a to state c along path abc?
W0/P0V0



(b) What is the following in going from b to c?
deltaE/P0V0



(c) What is the following in going through one full cycle?
deltaE/P0V0

(d) What is ΔS in going from b to c?
J/K

(e) What is ΔS in going through one full cycle?
J/K

Homework Equations

deltaS=Q/Tavg
deltaS=nRln(Vf/Vi)+nCvln(Tf/Ti)

The Attempt at a Solution

im not sure what the question is asking, or how to find information from the graph shown above, how do I start this one off?

 

[Andrew Mason]

The Attempt at a Solution

im not sure what the question is asking, or how to find information from the graph shown above, how do I start this one off?

In a), I think W0 refers to the work done by the gas in going from a to c. If so, calculate the work and divide by the product of initial pressure and initial volume (P0V0).

In b) you are supposed to calculate the change in internal energy (ΔE means ΔU = change in internal energy) in going from b to c. and then divide that by P0V0.

c) -> What is the change in internal energy over on complete cycle (ie when the system returns to its original state)?

d) To find ΔS you have to find the heat flow ΔQ and the temperature. How is dQ related to dU and dW? Express the temperature as a function of P and V.

e) -> Think of S as a state function.

AM

 

[tigers4]

a.) ok, W=nRTln(Vf/Vi)
p0v0=nRT
(nRTln(Vf/Vi))/nRT=ln(Vf/Vi)
b.) deltaEint=nCv(deltaT)
c.)0
d.)?
e.)0

 

[Andrew Mason]

a.) ok, W=nRTln(Vf/Vi)
p0v0=nRT
(nRTln(Vf/Vi))/nRT=ln(Vf/Vi)

You seem to be saying that T is constant. If T = PV/nR and P/nR is constant, T can't be constant as V changes. It is rather simple to find the work from a to b (\int PdV) since P is constant.

b.) deltaEint=nCv(deltaT)

What is \Delta T in terms of P0 and V0? (hint: use the ideal gas law: T = PV/nR)

c.)0
d.)?
e.)0

c and e are correct but you should explain. For d you have to find the heat flow from b to c. Since it is at constant volume (no work is done) what can you say about dQ and dU? What is dU in terms of dT? Once you work out the expression for dQ in terms of dT, divide by T to find dS and integrate from Tb to Tc.

AM