Homework Help: Thermodynamic Processes

1. The problem statement, all variables and given/known data

I can't aolve the following question:

Two moles of an ideal monoatomic gas trebles its initial volume in an isobaric expansion from state A to state B. The gas is then cooled isochorically to state C and finally compressed isothermally until it returns to state A. The molar gas constant is R = 8.314 J mol^–1K^–1 and Boltzmann's constant is 1.38 × 10–23 JK^–1.

If state B corresponds to a pressure P=8 atm (1 atm = 1.013 × 10⁵ Pa) and temperature T = 552°C, determine the temperature of the gas in state A.

Correct answer= 275.0K


2. Relevant equations

[tex]W=nRT ln \left( \frac{V_i}{V_f} \right)[/tex]

3. The attempt at a solution

I know that in an isothermal process the energy transfet [tex]Q[/tex] must be equal to the negative of the work done on the gas; [tex]Q=-W[/tex]. So to find the Temprature I must use the equation

[tex]W=nRT ln \left( \frac{V_i}{V_f} \right)[/tex]

I'm told that the amount of gas trebles but I don't know the initial volume of the gas, so I'm not sure if I can use this equation.

Another approach is maybe to find the change in temprature and then add it to the original temprature. So first I convert 552°C to Kelvins; 552+273.15=825.15 K. Then I want to use the equation [tex]Q=mc \Delta T[/tex]. But again I don't have the mass! What should I do?

Is my method even correct?

 

Hi,

[tex] PV=nRT[/tex]

[tex]\frac{PV}{T}=nR[/tex]

[tex]\frac{P_i V_i}{T_i}=\frac{P_fV_f}{T_f}[/tex]

[tex]\frac{V_i}{T_i}=\frac{V_f}{T_f}[/tex]

[tex]\frac{v_i}{552}=\frac{3(V_i)}{T_f}[/tex]

How am I supposed to evaluate T_f now when I don't know what the initial volume is?

 

Thanks a lot.