Question

A gas is compressed at a constant pressure of $50N/m^2$ from a volume of $10m^3$ to a volume of $4m^3.$ Energy of $100J$ 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
$\Delta V=V_2-V_1$
$=4-10=-6m^3$
As volume decreases, work is done on the gas and so it is negative
$W=p\Delta V$
$=50\times (-6)=-300J$
Heat supplied $Q=100J$
According to first law of thermodynamics change in internal energy is
$\Delta U=Q-W$
$=100-(-300)$
$=400J$
It means internal energy increase by $400J$