How Does Heat Addition Change the Temperature of an Ideal Gas?

[keemosabi]

Homework Statement

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?

Homework Equations

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.

 

[Andrew Mason]

[

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.

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

 

[keemosabi]

Doesn't it depend upon the gas?

 

[Andrew Mason]

Doesn't it depend upon the gas?

Not if it is an ideal gas, which this is. The specific heat is C_v = 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]<br /> <br /> regardless of the type of process.<br /> <br /> AM[/tex]