Find the Work Done and the Heat Transfer

[Northbysouth]

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Homework Statement

Air is compressed in a piston-cylinder assembly from p₁ = 10 lbf/in², T₁ = 500°R to a final volume of V₂ = 1ft³ in a process described by pv^1.25 = constant. The mass of air is 0.5 lb. Assuming ideal gas behavior and neglecting kinetic and potential energy effects, determine the work and heat transfer, each in Btu, using a) constant specific heats evaluated at 500°R and b) data from the table. Compare the results

The table is titled 'Ideal Gas properties of air

Homework Equations

C_v = constant

pv = nRT

Q = ΔE + W

E = U + KE + PE

W = ∫P dv

The Attempt at a Solution

I'm not sure where to begin with this question. I think I need to find the initial volume first but I'm not sure what the best way to do this is. I had thought to use:

pv = nRT

But then I'd have to convert my 0.5 lb of air into moles which would require me to convert everything else into English units. Is there a simpler way?

 

[Simon Bridge]

I'm not sure where to begin with this question.

Start with what you know about the kind of process that can be described as $pv^{1.25}=\text{const}$.

The only way to avoid converting things is to find an expression of the equations that uses the things you want.

 

[Chestermiller]

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Homework Statement

Air is compressed in a piston-cylinder assembly from p₁ = 10 lbf/in², T₁ = 500°R to a final volume of V₂ = 1ft³ in a process described by pv^1.25 = constant. The mass of air is 0.5 lb. Assuming ideal gas behavior and neglecting kinetic and potential energy effects, determine the work and heat transfer, each in Btu, using a) constant specific heats evaluated at 500°R and b) data from the table. Compare the results

The table is titled 'Ideal Gas properties of air

Homework Equations

C_v = constant

pv = nRT

Q = ΔE + W

E = U + KE + PE

W = ∫P dv

The Attempt at a Solution

I'm not sure where to begin with this question. I think I need to find the initial volume first but I'm not sure what the best way to do this is. I had thought to use:

pv = nRT

But then I'd have to convert my 0.5 lb of air into moles which would require me to convert everything else into English units. Is there a simpler way?

You need to find the value of the gas constant expressed in units of (psi)(ft³)/((lb-mole)(degree R)). Look it up with Google. Converting 0.5 lb to lb-moles is easy, since you just divide by 29. Then you are ready to apply the ideal gas law to calculate the initial volume in ft³.