Thermodynamics - engines question

[Jaydude]

I'm stuck on a question, part d below:

My attempt:

I reckon that T4 = T3 and T2 = T1, otherwise I don't know how else you can get T4 and T2...?

Once I got first part of d, I reckon I could do efficiency using part c that I derived.

I don't see where I'm supposed to use compression ratios in this question, if someone can direct me to the right path please!

(If this is supposed to be in advanced physics section, please let me know for next time!)

Kind regards,

Jay

 

[TSny]

Hello Jay. Welcome to PF!

I reckon that T4 = T3 and T2 = T1, otherwise I don't know how else you can get T4 and T2...?

You are given that $P_2V_2^\gamma = P_1V_1^\gamma$. See if you can use that along with the ideal gas law to express T₂ in terms of T₁, V₁ and V₂.

 

[Jaydude]

Sweet! But now I'm not sure how to get t4? And how do I apply that to get work done?

I could use my equation (correct) in part b but I don't know what Cp and Cv are, how do I apply the constant 1.4 there?

(I'm going to assume t2 is correct here...)

Thanks!

 

[TSny]

Try a similar calculation to find T₄ in terms of T₃.

 

[Jaydude]

Hello Jay. Welcome to PF!You are given that $P_2V_2^\gamma = P_1V_1^\gamma$. See if you can use that along with the ideal gas law to express T₂ in terms of T₁, V₁ and V₂.

Try a similar calculation to find T₄ in terms of T₃.

But I don't have V3/V4 compression ratio :(

 

[TSny]

But I don't have V3/V4 compression ratio :(

How is V₄ related to V₁? How is V₃ related to V₂?

 

[Jaydude]

I see what you did there, but I get the incorrect answer, T4 should be 1379k

What have I done wrong ?

 

[TSny]

How do you justify taking V₄ / V₃ to be 16?

 

[Jaydude]

How is V₄ related to V₁? How is V₃ related to V₂?

How do you justify taking V₄ / V₃ to be 16?

If V4 = V1 and V3 = V2, and we know V1/V2 = 16, then V4/V3 = 16 too...?

 

[Jaydude]

I see my problem.

V2 does not equal V3!

Can't solve this, its getting annoying as I've spent hours ripping my hair out on this!

 

[Jaydude]

Bump. Can Someone point me in the right direction here/helpout with the solution? This is only for my practise and is not part of any H/W or Cwk and all of my friends are struggling with this Q too.

Kind regards,
Jay

 

[TSny]

V2 does not equal V3, but you can express V3 in terms of V2 using the ideal gas law.