Question

A gas under constant pressure of $ 45 \times 10^5\, p_a $ when subjected to $ 800 \,k j $ of heat, changes the volume from $ 0.5\, m^3 $ to $ 2.0\, m^3 $ . The change in internal energy of the gas is

• A. $ 6.75 \times 10^5 \,J $
• B. $ 5.25 \times 10^5 \,J $
• C. $ 3.25 \times 10^5 \,J $
• D. $ 1.25 \times 10^5 \,J $

Answer 1

Answer: (D)

Given, $p = 4.5 \times 10^2\, Pa$
$dQ =800 \,kJ$
$= 800 \times 10^3 \,J$
Change in volume $= (2.0 - 0.5) m^3$
$= 1.5 \,m^3$
From first law of thermodynamics,
$dQ = dU + p \cdot dV$
$dU = dQ - p \cdot dV$
$= 800 \times 10^3 - 4 .5 \times 10^5 \times 1.5$
$= - 1.25 \times 10^5\, J$
Change in internal energy
$(V)= 1.25 \times 10^5\, J$.