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

  • Thread starter Ghodsi
  • Start date
  • Tags
    Cv
In summary, the conversation discusses the calculation of Cv for an ideal gas that is compressed adiabatically to one-half of its original volume, resulting in a temperature increase from 273 to 433K. Assuming Cv is independent of temperature, the value of Cv is calculated using the equations Cv = dU/dT and dU = dq + dw, where dq = 0 for adiabatic processes. The value of Cv is found to be -nR*ln(1/2), and additional equations are suggested for further verification and calculation.
  • #1
Ghodsi
4
0

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?)
 
Last edited:
Physics news on Phys.org
  • #2
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.
 
  • #3
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.
 
  • #4
Yeah.
 
  • #5
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
 
  • #6
Thanks guys. This is pretty crucial assistance.
 
  • #7
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.
 

1. What is Cv and how is it related to T & V?

Cv stands for "coefficients of variation" and is a statistical measure that represents the ratio of the standard deviation to the mean in a dataset. T & V, on the other hand, refer to temperature and volume. Cv is used to calculate the flow rate of a fluid based on its temperature and volume.

2. Why is it important to calculate Cv?

Calculating Cv is important in various engineering and scientific fields, particularly in fluid mechanics. It helps to determine the flow rate of a fluid, which is essential in designing and optimizing systems such as pipelines, pumps, and valves. Cv also allows for comparisons between different fluids and their flow rates.

3. How do you calculate Cv from T & V?

The formula for calculating Cv from T & V is: Cv = Q/SQRT((T1+T2)/2) x V, where Q is the flow rate, T1 and T2 are the inlet and outlet temperatures, and V is the volume. This formula can be simplified in some cases, such as when the temperature difference is small, to Cv = Q/(T1-T2) x V.

4. Can you provide an example of calculating Cv from T & V?

Sure, let's say we have a fluid flowing through a pipe with a volume of 10 cubic meters and a temperature difference of 50 degrees Celsius between the inlet and outlet. If the flow rate is 5 cubic meters per second, the calculation would be: Cv = 5/SQRT((50+50)/2) x 10 = 12.5. This means that the Cv for this fluid is 12.5 and can be used to determine the flow rate in other similar systems.

5. Are there any limitations to using Cv to calculate flow rate?

Yes, there are some limitations to using Cv. It assumes that the fluid is incompressible, the flow is laminar, and the system is in steady state. If any of these assumptions are not met, the calculated flow rate may not be accurate. It is important to also consider other factors such as pressure and viscosity when calculating flow rate.

Similar threads

  • Biology and Chemistry Homework Help
Replies
11
Views
3K
Replies
1
Views
533
  • Biology and Chemistry Homework Help
Replies
2
Views
3K
  • Biology and Chemistry Homework Help
Replies
2
Views
1K
  • Mechanical Engineering
Replies
1
Views
1K
  • Biology and Chemistry Homework Help
Replies
4
Views
6K
  • Advanced Physics Homework Help
Replies
5
Views
956
  • Biology and Chemistry Homework Help
Replies
1
Views
6K
  • Introductory Physics Homework Help
Replies
9
Views
5K
  • Thermodynamics
Replies
20
Views
1K
Back
Top