# Thermodynamics of gases

## 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.

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

i did!

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. $$v_{f},T_{f}$$)

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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

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

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