How Is Internal Energy Calculated for an Ideal Gas Using Temperature Change?

[tuki]

Homework Statement

1.5 moles of two atom ideal gas is being heated so that pressure and volume change during the process. At the beginning pressure is at 336 kPa and volume is 12 Liters. In the end pressure is 439 kPa and volume is 14 Liters. What is change in internal energy?

Relevant Equations

Definition of change in internal energy
$$ \Delta U = Q - W $$
Work done by pressure
$$ W = \int_{V_1}^{V_2} p dV $$

I have the definition of change in internal energy.
$$ \Delta U = Q - W $$
I can get the work by
$$ W = \int_{V_1}^{V_2} p dV = p \Delta V $$
however the pressure isn't constant so this won't do.
$W$ is work done by the gas and $Q$ is amount of heat energy brought into the system.
I'm not quite sure how do i get these? I think I'm stuck.

 

[Chestermiller]

You don't (and can't) use the first law to do this because all you are given is the end points, but not the pressure and volume changes in between. So you must solve this problem only having the end point information.

What is the change in internal energy of an ideal gas in terms of its change in temperature?
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