- #1

castrodisastro

- 82

- 0

## Homework Statement

An ideal gas is enclosed in a cylinder with a movable piston at the top. The walls of the cylinder are insulated, so no heat can enter or exit. The gas initially occupies volume

**V**and has pressure

_{1}**p**and temperature

_{1}**T**. The piston is then moved very rapidly to a volume of

_{1}**V**. The process happens so rapidly that the enclosed gas does not do any work.

_{2}=8.5V_{1}Find

**p**,

_{2}**T**, and the change in entropy of the gas. [Express your answers in terms of

_{2}**p**,

_{1}**T**,

_{1}**n**, and

**R**.]

## Homework Equations

**p**

pV=nRT

ΔS=nRln(V

_{1}V_{1}=p_{2}V_{2}pV=nRT

ΔS=nRln(V

_{f}/V_{i})## The Attempt at a Solution

To determine

**p**I used the relationship

_{2}**p**

_{1}V_{1}=p_{2}V_{2}**p**

_{2}=(p_{1}V_{1})/V_{2}**p**

_{2}=(p_{1}V_{1})/(8.5V_{1})**p**

_{2}=(p_{1})/8.5To determine

**T**we see that the process itself is an isothermal process since no work was done, and no heat escaped,

_{2}**Q=W**. So the temperature will not have changed.

**T**

_{2}=T_{1}I can't seem to determine

**ΔS**correctly. Since the process is an isothermal expansion, the change in entropy is given by the equation

**ΔS=nRln(V**

_{2}/V_{1})from this I can substitute

**8.5V**for

_{1}**V**, resulting in

_{2}**ΔS=nRln((8.5)V**

_{1}/V_{1})**ΔS=nRln(8.5)**

This answer however, is incorrect. The problem asks to put in the answer in terms of

**p**,

_{1}**T**,

_{1}**n**,

**R**. The format of this question is a blank field that allows me to create an equation with subscripts, superscripts, fractions, matrices, etc. FYI.

Any help is appreciated, thanks in advance.