Change in internal energy for an isobaric process?

[erik-the-red]

Question:

When a quantity of monatomic ideal gas expands at a constant pressure of $$4.00 \times 10^{4} {\rm Pa}$$, the volume of the gas increases from $$2.00 \times 10^{ - 3} {\rm m}^{3}$$ to $$8.00 \times 10^{ - 3} {\rm m}^{3}$$.

A.

What is the change in the internal energy of the gas?

It's isobaric, so the pressure is constant.

I know the work is $$P\Delta V = (4.00 * 10^4)(6.00 * 10^{-3})$$.

But, I don't know how to get $$\Delta U$$ from this.

 

[Physics Monkey]

What variables does the internal energy of the ideal gas depend on? How do these variables change in the aforementioned process?

 

[erik-the-red]

OK, the internal energy depends only on temperature.

For a monatomic gas, $$\Delta U = \frac{3}{2}nR\Delta T$$.

I don't know the number of moles or the change in temperature.

 

[Physics Monkey]

Progress! Ok, so now you need to know the change in temperature times $$n R$$, right? You know the pressure and volume of the gas at two different points in P,V space. Can you use this information to find the unknown? Hint: ideal gas law.

 

[mezarashi]

This relationship should be helpful as well.

$$\Delta U = Q - W$$

Apparently you have the equation for the W right. Now use the ideal gas law and a bit of calorimetry.

 

[erik-the-red]

Thanks a lot!