Question

During adiabatic expansion process, if the temperature of 4 moles of a monoatomic gas is decreased by \(100^\circ C\), then the work done by the gas is
(Universal gas constant \(R = 8.3 \, \text{J/mol·K}\))

• A. \(4150 \, \text{J}\)
• B. \(8300 \, \text{J}\)
• C. \(2490 \, \text{J}\)
• D. \(4980 \, \text{J}\)

Hint:

For monoatomic gases, use \( \gamma = \frac{5}{3} \) in adiabatic work formula \( W = \frac{nR \Delta T}{\gamma - 1} \).

Answer 1

The Correct Option is D

Work done in adiabatic process for monoatomic gas: \[ W = \frac{nR \Delta T}{\gamma - 1}, \quad \text{where} \quad \gamma = \frac{5}{3} \] \[ \Delta T = 100\, \text{K},\quad n = 4, \quad R = 8.3 \Rightarrow W = \frac{4 \cdot 8.3 \cdot 100}{\frac{5}{3} - 1} = \frac{3320}{\frac{2}{3}} = 4980 \, \text{J} \]