Question

An ideal monatomic gas is supplied 80 joule heat atconstant pressure. The increase in internal energyof gas, is

Answer 1

Given Data:

At constant pressure heat supplied, $Q=80J$

For ideal monoatomic gas, $C_v=\frac{3R}{2}$

Step 1: Increase in internal energy:

​Work done, $W=P\Delta V=nR\Delta T$

Change in internal energy, $W=P\Delta V=nR\Delta T$

By first law of thermodynamics;

$Q=W+\Delta U$

$80=nR\Delta T+\frac{3}{2}nR\Delta T$

$80=\frac{5nR\Delta T}{2}⟹nR\Delta T=32$

We know.

$\Delta U=n{C}_v\Delta T$

$\Delta U=n\left(\frac{3}{2}R\right)\Delta T$

$\Delta U=\frac{3}{2}nR\Delta T⟹\Delta U=\frac{3}{2}\times 32=48J$

So,

Increase in internal energy, $=48J$