Thermodynamic Application Isothermal Work

[latitude]

Homework Statement

One mole of an ideal gas does 3000 J work on its surroundings as it expands isothermally to a final pressure of 1 atm and volume 25 L. Determine a) initial volume and b) Temp of gas

Homework Equations

The Attempt at a Solution

Well, its isothermal, so Temp is constant, so
W = nRTln(vi/vf)
It says it expands, so the initial volume is <25 L...
that's kinda all I got right now; I'm not sure how to get the next step, since both T and vi are in the equation. It must have something to do with pressure.

 

[Andrew Mason]

Homework Statement

One mole of an ideal gas does 3000 J work on its surroundings as it expands isothermally to a final pressure of 1 atm and volume 25 L. Determine a) initial volume and b) Temp of gas

Homework Equations

The Attempt at a Solution

Well, its isothermal, so Temp is constant, so
W = nRTln(vi/vf)
It says it expands, so the initial volume is <25 L...
that's kinda all I got right now; I'm not sure how to get the next step, since both T and vi are in the equation. It must have something to do with pressure.

How do you find the temperature of the gas? Find that and then determine what ln(vi/vf) has to be if W=3000J.

AM

 

[latitude]

PV = nRT
(1.013 x 10^5)(10 m^3) = (1)(8.314)T
T = Some really big, way illogical number? Unless the moles thing is wrong...

ARGH. This one is frustrating me. I'm wondering if I don't have to find volume first??

 

[latitude]

Oooh...

3000 J = nR(PV/nR)(ln(vi/vf))
3000 J = (10.13 x 10^5)(25 L) ln(vi/25)
1.184 x 10^-3 = vi/25
vi = 0.029 L??

Possible??

EDIT: No, cause my final temp is still 304606.7 K !

 

[Andrew Mason]

Oooh...

3000 J = nR(PV/nR)(ln(vi/vf))
3000 J = (10.13 x 10^5)(25 L) ln(vi/25)
1.184 x 10^-3 = vi/25
vi = 0.029 L??

Possible??

EDIT: No, cause my final temp is still 304606.7 K !

Start with PV=nRT

$$P_iV_i = nRT = P_fV_f$$

You know $P_f, V_f$ and n so work out T. Be careful to use the correct units for volume. Units are litres or 10^-3 m^3.


Then, from W = nRTln(vi/vf), work out what vi is.

AM