Can you write the ideal gas law this way?

[mm2424]

Homework Statement

Calculate the work done in an adiabatic process where P1 = 1.2 atm, V1 = 0.2 m^3, P2 = 2.4 atm and V2 = 0.117 m^3

Homework Equations

W=-nCvΔT
PV=nRT

The Attempt at a Solution

I tried to group the work formula as follows:
W=-(nΔT)Cv

and then tried to rewrite the ideal gas law the following way:

ΔPΔV=nRΔT
nΔT = (ΔPΔV)/R

then I rewrote the Work equation as

W=-Cv(ΔPΔV)/R

However, this did not yield the correct answer. I imagine the problem arises in my rewriting of the ideal gas law...is it never ok to express the ideal gas law in this way?

Thanks!

 

[ehild]

Homework Equations

W=-nCvΔT
PV=nRT

I tried to group the work formula as follows:
W=-(nΔT)Cv

and then tried to rewrite the ideal gas law the following way:

ΔPΔV=nRΔT

You can not write the ideal gas low in that way! For a very little step, you can write nRdT = d(PV)=dP V+dV P. Both P and V change during the process, so the factors of dV and dP are not constants. They are functions.

So it is better to use the basic equation for change of the internal energy in the adiabatic process Δ U= -W(gas), that is Cvn(T2-T1)=-W(gas)
Determine T1 a and T2 from the given P and V data using the ideal gas law, PV=nRT, and substitute them in the equation for W(gas)ehild