How can I calculate the work done in a gas compression problem?

[BrainMan]

Homework Statement

Homework Equations

ΔE_th = nC_vΔT

W = -∫ p dV

pV = nRT

The Attempt at a Solution

I tried to find the total change in thermal energy by finding the temperature change.

I first found the initial pressure

P₁ = nRT/V = 32464.4 Pa

Then I solved for the final pressure

p₁V₁² = p₂V₂²

p₁V₁² / V₂² = p₂ = 292179.6 Pa

Then I found the final temperature

T₂ = pV/nR = 879 K

What I wanted to do next was use ΔE_th = nC_vΔT to find the total thermal energy and then subtract the work to find the heat. Unfortunately, I don't know what C_v is equal to or how to find the work.

 

[Chestermiller]

What is Cv for a diatomic gas? What is the general equation for the amount of P-V work done on the surroundings?

 

[BrainMan]

What is Cv for a diatomic gas? What is the general equation for the amount of P-V work done on the surroundings?

C_v is one the things that is confusing me. In my book it has a table for a couple of C_v's for different gases so I'm not sure which to use.

https://lh3.googleusercontent.com/Rv3s5lQ2vyLKOnlbAg64OHbFcNAw_pmlo3t_v1YoFHulQit7hmXE3QNfhnkkY2CkbFphumXv2Fur1BgU6j7CJ2ndcsMKnvvKsKTcS0La7W1cMEUdeQQ3FbwVGqP5uWtq6m-kac0EcRYm_z-pHDVDPFX_KTcGziQOZQlpRX-c_lkY1xWJEPMQcEwFIdgZ7kYoCr9xMVr0IzzS4h_1xe3yKY4GOsox4ARm5AfFURq_crZHRoHdsGH9XYU8hyrFe2AFoDavbMAn2ee_h3yrviHDKjvCau1GbRp6K7xKT5ql1j64izFwZO32BxrpXCMhI5CEMjMnIc5hN6-259RsF8SsgIiZxsnQD7TAu3-9d8Xj3vMR35dMFtUUSelQQqWnQblf0ylCU0DYrzG9N2Mfx3g3_WlsPUZkkoEKP9dmSO8HU0KEfev7mT2Xz8cB2mcGLaFXeywOdi0kWonRkAfn1XG3mGgT2S4j0GWWMPL-AZpMb5RgzYHMe_HFK0oKB18wEPGsX3PAGwTh8yoklqY_TLssNCRJeLLKTYIhXf1Pl7LHumgHEHRrhfuHt0ZtmZ5AEQKq64Nooh5rsHMRfAGXyvQP6SdsadwWXxxc2evTNwlvnTGZRg9ucT4P=w619-h662-no

 

[Chestermiller]

For an ideal diatomic gas, the molar Cv is equal to 5R/2. Did they not cover this in your course?

 

[BrainMan]

For an ideal diatomic gas, the molar Cv is equal to 5R/2. Did they not cover this in your course?

I looked ahead and it seems it will be covered in the next chapter. OK so that solves that problem. What I'm wondering about now is the work. My book wasn't very clear about work and the two ways it gave to calculate work were to W = -∫ p dV or to find the area under the curve of the pV diagram.

 

[Chestermiller]

I looked ahead and it seems it will be covered in the next chapter. OK so that solves that problem. What I'm wondering about now is the work. My book wasn't very clear about work and the two ways it gave to calculate work were to W = -∫ p dV or to find the area under the curve of the pV diagram.

The equation you wrote for the work represents the work done by the surroundings on the system. This equation is correct. You are aware that the integral of PdV is the same as the area under the curve of the pV diagram, correct? In this problem, to get the work, you are going to have to integrate pdV.