# 1st Law of Thermodynamics

1. Jan 19, 2009

### keemosabi

1. The problem statement, all variables and given/known data
Three moles of an ideal monatomic gas are at a temperature of 345 K. Then, 2114 J of heat are added to the gas, and 811 J of work are done on it. What is the final temperature of the gas?

2. Relevant equations

3. The attempt at a solution
I have a feeling I'm missing an equation. I thought the equation was U = Q - W but that won't help me here.

2. Jan 19, 2009

### Andrew Mason

How is U related to temperature? Hint: what is the specific heat of a monatomic gas at constant volume (where W = 0 so Q = U)?

AM

3. Jan 20, 2009

### keemosabi

Doesn't it depend upon the gas?

4. Jan 20, 2009

### Andrew Mason

Not if it is an ideal gas, which this is. The specific heat is Cv = 3R/2 where R is the universal gas constant (units are J/mole K). Since, by definition, $\Delta Q = nC_v\Delta T$ and $\Delta U = \Delta Q$ for a constant volume process and since U is a function only of T, it follows that

[tex]\Delta U = nC_v\Delta T[/itex]

regardless of the type of process.

AM