Question

A gas is compressed from a volume of $2 \,m^3$ to a volume of $1\, m^3$ at a constant pressure of $100\, N/m^2$. Then it is heated at constant volume by supplying $150\, J$ of energy. As a result, the internal energy of the gas :

• A. Increases by 250 J
• B. Decreases by 250 J
• C. Increases by 50 J
• D. Decreases by 50 J

Answer 1

Answer: (A)

Increases by 250 J

Answer 2

The correct answer is (A) : Increases by 250 J
As we know,
$\Delta Q = \Delta u+\Delta w$
($I^{st}$ law of thermodynamics)
$\Rightarrow \Delta Q = \Delta u+P\Delta v$
or $150 = \Delta u+100\left(1-2\right)$
$= \Delta u-100$
$\therefore \Delta u = 150+100 = 250J$
So, the internal energy of the gas increases by $250\, J$