Question regarding change in internal energy

[erik-the-red]

A cylinder contains 0.0100 mol of helium at T = $$27.0 ^\circ \text{C}$$.

If the presure of the helium is kept constant, how much heat is needed to raise the temperature from 27.0 to 67.0 C?

If the gas is ideal, what is the change in its internal energy?

I got the answer for the first part correct.

My question involves some concepts.

It is because helium is monatomic that the $$C_v$$ in $$\Delta U = nC_{v}\Delta T$$ is $$\frac{3}{2}R$$, correct?

 

[Andrew Mason]

A cylinder contains 0.0100 mol of helium at T = $$27.0 ^\circ \text{C}$$.
If the presure of the helium is kept constant, how much heat is needed to raise the temperature from 27.0 to 67.0 C?
If the gas is ideal, what is the change in its internal energy?
I got the answer for the first part correct.
My question involves some concepts.
It is because helium is monatomic that the $$C_v$$ in $$\Delta U = nC_{v}\Delta T$$ is $$\frac{3}{2}R$$, correct?

Correct.

AM

 

[erik-the-red]

So, if the volume was kept constant and the temperature was changed by the same interval, the change in internal energy would still be given by $$\Delta U = nC_{v}\Delta T$$ with $$C_{v} = \frac{3}{2}R$$?

 

[Andrew Mason]

So, if the volume was kept constant and the temperature was changed by the same interval, the change in internal energy would still be given by $$\Delta U = nC_{v}\Delta T$$ with $$C_{v} = \frac{3}{2}R$$?

The change in internal energy is always this. You don't have to keep the volume constant. It is just that if the volume is constant there is no work done and all the heat is used to increase internal energy so $$Q = \Delta U = nC_{v}\Delta T$$.

AM