Ideal gas temperature and pressure in a rigid insulated box

[Nenad]

Help! - (Ideal gas temp problem)

Im having a problem with this question, on my chem assignement. Here it is:

Q: A rigid, constant volume box contains a monoatomic ideal gas initially at 20 degrees Celsius and at 200kPa. The box is completely insulated. A 100-watt electric heater is used to heat the gas in the box. After 10 minutes of heating the pressure in the box rises to 300kPa. Calculate the volume of the box, in cubic meters.

Is it A)0.24 B)0.40 C)0.67 D)1.00 E)1.50

Ive tried using the ideal gas law $$PV = nRT$$, and solving for $$T_2$$. But this gets me nowere, I just am left with a ratio of volumes and in the end I get $$V_1 = v_2$$. I have also tried using unit conversion and seeing how many Joules were placed in the box by heationg it, but I get an answer for volume of $$0.2m^3$$.
If somebody could give me a hint on what to do, that would be great.

 

[Tide]

Do you have a formula relating the internal energy of an ideal gas to its temperature?

 

[Nenad]

nope, but I would shure like to know one. Any hints?

 

[Tide]

Sure. How about this one?
$$U = \frac {3}{2}N k_B T$$

 

[Nenad]

what do the variables stand for?

 

[Tide]

U is the internal energy.
N is the total number of atoms/molecules.
T is temperature.
$k_B$ is the Boltzmann constant.

 

[Nenad]

my prof told me there is an easier way to do it than this.