I'm working on a Thermodynamics question on Work Done during compression. The book gives proof for a formula but I can't seem to follow one step of it.

We are working with pressure,volume and temperature at different stages of compression. M is mass and R is the gas constant

basic formulas are P1V1=MRT1 or P2V2=MRT2 (1)
and t2/t1=[(p2/p1)^(n-1)/n]=[(v1/v2)^(n-1)] (2)
where n=index of compression for a polytropic process.

I'm not sure if you need this extra info because it is a regular algebra substitution problem that I have.

work done per cycle
n/(n-1) (p2v2-p1v1)Which I do understand (3)
n/n-1 mr(t2-t1) Which I do understand (4)
n/n-1 mrt1{t2/t1 - 1}don't understand. (5)
Are they dividing through by 1/t1 inside the brackets? And how does the t1 get tacked onto the mr?
Is nmr(t2-t1)/n-1 the same as (4)?

After they get t2/t1 and mrt1 in the equation, they just substitute values from equation (1) and (2) to get 6 different forms of the main equation

i.e. n/n-1 mrt1[{v1/v2}^n-1 -1] or
n/n-1 p1v1[{p2/p1}^n-1/n -1]
so that's no problem
I'm just not following the step from (4) to (5)
I'm assuming it's not a book typo.
Thanks for any help you can give me.
Daren

Hi,

Start with equation (5). By multiplying through, you get equation (4).