Thermodynamic Processes

[roam]

Homework Statement

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

Homework Equations

$$W=nRT ln \left( \frac{V_i}{V_f} \right)$$

The Attempt at a Solution

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

$$W=nRT ln \left( \frac{V_i}{V_f} \right)$$

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 $$Q=mc \Delta T$$. But again I don't have the mass! What should I do?

Is my method even correct?

 

[Andrew Mason]

The volume at A is 1/3 of that at B. P is the same at A and B. Apply the ideal gas law to find T at A. It has to be 1/3 of the temperature at B.

AM

 

[roam]

The volume at A is 1/3 of that at B. P is the same at A and B. Apply the ideal gas law to find T at A. It has to be 1/3 of the temperature at B.

AM

Hi,

$$PV=nRT$$

$$\frac{PV}{T}=nR$$

$$\frac{P_i V_i}{T_i}=\frac{P_fV_f}{T_f}$$

$$\frac{V_i}{T_i}=\frac{V_f}{T_f}$$

$$\frac{v_i}{552}=\frac{3(V_i)}{T_f}$$

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

 

[Andrew Mason]

$$\frac{V_i}{T_i}=\frac{V_f}{T_f}$$

$$\frac{v_i}{552}=\frac{3(V_i)}{T_f}$$

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

?? Divide by Vi - it disappears. (You don't have to find the initial volume. You just need to know Vf/Vi = 3)

$$\frac{V_i}{T_i}=\frac{V_f}{T_f}$$

$$\frac{T_f}{T_i}=\frac{V_f}{V_i} = 3$$

$$T_i = \frac{T_f}{3}$$

Further hint: temperatures have to be converted to.....

AM

 

[roam]

Thanks a lot.