Temperature and Entropy of an ideal gas

[moonkey]

Homework Statement

One mole of an ideal gas is confined to a vessel of volume 4L at a temperature of 300°C. The vessel is placed inside a container of volume 200L and the gas is released.

(a) What is the final temperature of the gas if it's expansion into the container is adiabatic?

(b) What would be the change in entropy if the expansion were isothermal?

Homework Equations

The Attempt at a Solution

Not worth showing. I've been at this question and four others for more than 10hours over the last two days and I only have one of them done. I'd appreciate any helpful hints.

 

[The legend]

do you know what the relevant equations are?
If you do, then you can quite easily solve the problem knowing
v1, t1, v2...you can find t2.

 

[Andrew Mason]

Homework Statement

One mole of an ideal gas is confined to a vessel of volume 4L at a temperature of 300°C. The vessel is placed inside a container of volume 200L and the gas is released.

(a) What is the final temperature of the gas if it's expansion into the container is adiabatic?

(b) What would be the change in entropy if the expansion were isothermal?

Homework Equations

The Attempt at a Solution

Not worth showing. I've been at this question and four others for more than 10hours over the last two days and I only have one of them done. I'd appreciate any helpful hints.

Start by answering these questions (assume the 200L container is empty to start):

1. Does the gas do any work in expanding into the 200L space?

2. Apply the first law. If there is no heat flow (adiabatic) what is the change in internal energy? That will give you the change in temperature: $\Delta U = nC_v\Delta T$

3. To calculate the change in entropy you have to determine integral of dQ/T over the reversible path between the beginning and end state. In the reversible path, the gas would maintain constant temperature but it would be doing work. So what is the expression for dQ?

AM