Calc Cv from T & V: How to Calculate Cv Homework

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Discussion Overview

The discussion revolves around calculating the specific heat at constant volume (Cv) for an ideal gas undergoing an adiabatic compression. Participants explore various approaches and equations related to thermodynamics, specifically focusing on the relationship between temperature, volume, and work done during the process.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant states the initial conditions and equations for an ideal gas undergoing adiabatic compression, expressing uncertainty about whether to use initial or final values for temperature and volume.
  • Another participant proposes a method involving the work done during the process, leading to a derived expression for Cv, but expresses doubt about its correctness.
  • A third participant suggests using the relationship T1/T2 = (V2/V1)^(γ-1) to find γ, and then relates Cp and Cv using the equation Cp - Cv = R, indicating a potential path to eliminate Cp to find Cv.
  • Several participants express uncertainty about their calculations and seek confirmation or alternative methods to approach the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct method to calculate Cv, with multiple competing approaches and expressions presented. There is ongoing uncertainty regarding the application of equations and the values to use in calculations.

Contextual Notes

Limitations include assumptions about Cv being independent of temperature and the dependence of results on the correct application of adiabatic process equations. The discussion also reflects varying levels of confidence in the proposed solutions and methods.

Who May Find This Useful

This discussion may be useful for students studying thermodynamics, particularly those working on problems involving ideal gases and adiabatic processes.

Ghodsi
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Homework Statement



When one mole of an ideal gas is compressed adiabatically to one-half of its original volume, the temperature of the gas increases from 273 to 433K. Assuming that Cv is independent of temperature, calculate the value of Cv for this gas.

Homework Equations



Cv = dU/dT
dU = dq + dw
dq = 0 for adiabatic processes, thus dU=dw
PV = nRT

The Attempt at a Solution



Cv = -pdV / dT
Cv = (-nRT/V)(dV/dT)

I'm stuck here.
Assuming I'm correct thus far, do I use the initial or final values for T and V (i.e. do I use 273K or 433K?)
 
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I think we might be in the same class...

I've been trying to verify my solution, but no luck so far. This is what I got:

Cv = (dU/dT)
dU = dq + dw, but dq = 0, so dU = dw and Cv = dU/dT

w = -nRTln(V2/V1), but V2 = 1/2V1, so w = -nRTln(1/2), and dw = -nR*ln(1/2)*dT

Substitute the last equation for dw in Cv=dw/dT and you get Cv = -(nR*ln(1/2)*dT)/dT which simplifies to Cv = -nR*ln(1/2).

That's what I got, but I'm not confident that it's correct.
 
Elber 10am MWF?
beet said:
I think we might be in the same class...

I've been trying to verify my solution, but no luck so far. This is what I got:

Cv = (dU/dT)
dU = dq + dw, but dq = 0, so dU = dw and Cv = dU/dT

w = -nRTln(V2/V1), but V2 = 1/2V1, so w = -nRTln(1/2), and dw = -nR*ln(1/2)*dT

Substitute the last equation for dw in Cv=dw/dT and you get Cv = -(nR*ln(1/2)*dT)/dT which simplifies to Cv = -nR*ln(1/2).

That's what I got, but I'm not confident that it's correct.
 
Yeah.
 
Ghodsi said:

Homework Statement



When one mole of an ideal gas is compressed adiabatically to one-half of its original volume, the temperature of the gas increases from 273 to 433K. Assuming that Cv is independent of temperature, calculate the value of Cv for this gas.


Homework Equations



Cv = dU/dT
dU = dq + dw
dq = 0 for adiabatic processes, thus dU=dw
PV = nRT


The Attempt at a Solution



Cv = -pdV / dT
Cv = (-nRT/V)(dV/dT)

I'm stuck here.
Assuming I'm correct thus far, do I use the initial or final values for T and V (i.e. do I use 273K or 433K?)
I think you should use
T1/T2 = (V2/V1)^γ-1
then you also find the value of
P1 and P2 from
P1V1^γ= P2V2^γ

The put the values in adiabatic process equation
∂W = (P1V1-P2V2)/γ-1
Then use your formulae
 
Thanks guys. This is pretty crucial assistance.
 
Meemo said:
I think you should use
T1/T2 = (V2/V1)^γ-1

Find γ from the above. Then use:

Cp-Cv = R (gas constant)
(Cp/Cv) = γ

Eliminate Cp from these two equations to get Cv.
 

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