What Are the Final Pressure and Temperature of an Adiabatic Gas Compression?

[terry2112]

Homework Statement

A mass of gas occupies a volume of 4.3L at a pressure of 1.2 atm and a temperature of 310K. It is compressed adiabatically to a volume of 0.76L.Determine (a)the final pressure and (b) the final temperature,assuming the gas to be an ideal gas for which gamma = 1.4.

Homework Equations

gamma = Cp/Cv
w = (1/gamma-1)(p1v1-p2v2)
w=-Cv(deltaT)

The Attempt at a Solution

I'm not really sure where to start but haf wote out everything and have converted all to basic SI units,explanation of solution of this question would be much appreciated.

 

[konthelion]

First start out by writing all of the given information in terms of those variables.

 

[terry2112]

i did!

 

[konthelion]

No you did not. As far as I can see, you didn't show any work.. you just stated the problem and showed some equations.

Let $$v_{i}=4.3L,p_{i}=1.2atm,T_{i}=310K$$ etc. Now write the remaining given information in this format so that you can clearly see what are known and unknown variables(i.e. $$v_{f},T_{f}$$)

 

[terry2112]

V1 = 0.0043m^3,P1=121560Pa,T1=310K then goes through an adiabatic compression

to

V2=0.00076m^3,P2=?,T2=?

given gamma = 1.4

 

[konthelion]

Since this is a adiabatic process, Q=0 so for some constant K, $$K=PV^{\gamma}$$
then, $$\frac{p_{2}}{p_{1}}=\left(\frac{v_{1}}{v_{2}}\right)^\gamma$$ where subscript 2 means final state, subscript 1 means initial state.

and $$\frac{T_{2}}{T_{1}}=\left(\frac{v_{1}}{v_{2}}\right)^{\gamma-1}$$