Question

A gas is compressed at a constant pressure of $50\, N / m ^{2}$ from a volume of $10\, m ^{3}$ to a volume of $4\, m ^{3} .$ Energy of $100\, J$ is thus added to the gas by heating. Its internal energy is

• A. decreased by 200 J
• B. increased by 100 J
• C. increased by 300 J
• D. increased by 400 J

Answer 1

Answer: (D)

Change in volume
$\Delta V= V_2 - V_1$
$=4-10= -6\, m^3$
As volume decreases, work is done on the gas and so it is negative
$W=p\Delta V$
$=50 \times(-6)=-300\, J$
Heat supplied $Q = 100\, J$
According to first law of thermodynamics change in internal energy is
$\Delta U=Q-W$
$= 100-(-300)$
$= 400\, J$
It means internal energy increase by $400\, J$