Q21 / 150 · MHT CET 2026 (20 April Shift 2) · Chemistry
Calculate the change in internal energy if an ideal gas expands from $0.5\ \text{dm}^3$ to $3.5\ \text{dm}^3$ at constant pressure 2 bar by absorbing 1800 J heat energy.
- Correct answerA$1200$ J.
- B$-1200$ J.
- C$2400$ J.
- D$-2400$ J.
Solution
Given $V_1 = 0.5\ \text{dm}^3$, $V_2 = 3.5\ \text{dm}^3$, $P = 2\ \text{bar}$, and heat absorbed $q = 1800\ \text{J}$.
Work done during expansion at constant pressure is given by $W = -P(V_2 - V_1)$.
$W = -2 \times (3.5 - 0.5) = -6\ \text{bar}\cdot\text{dm}^3$
Since $1\ \text{bar}\cdot\text{dm}^3 = 100\ \text{J}$, we have $W = -600\ \text{J}$.
According to the first law of thermodynamics, $\Delta U = q + W$.
Substituting the values, $\Delta U = 1800 - 600 = 1200\ \text{J}$.
Answer: $1200$ J.
Work done during expansion at constant pressure is given by $W = -P(V_2 - V_1)$.
$W = -2 \times (3.5 - 0.5) = -6\ \text{bar}\cdot\text{dm}^3$
Since $1\ \text{bar}\cdot\text{dm}^3 = 100\ \text{J}$, we have $W = -600\ \text{J}$.
According to the first law of thermodynamics, $\Delta U = q + W$.
Substituting the values, $\Delta U = 1800 - 600 = 1200\ \text{J}$.
Answer: $1200$ J.
Hence, the correct answer is option: 'A'.