JEE Mains · Physics · STD 11 - 11. thermodynamics
A certain gas is isothermally compressed to \(\left(\dfrac{1}{3}\right)^{rd}\) of its initial volume (\(V_o = 3\) litre) by applying required pressure. If the bulk modulus of the gas is \(3 \times 10^5\) N/m\(^2\), the magnitude of work done on the gas is _______ J.
- A 989
- B 1089
- C 889
- D 789
Answer & Solution
Correct Answer
(A) 989
Step-by-step Solution
Detailed explanation
For an isothermal process, the isothermal bulk modulus equals the gas pressure: \(B_T = -V\dfrac{dP}{dV}\) Since \(PV = \text{constant}\), differentiating gives \(P\,dV + V\,dP = 0\), so \(\dfrac{dP}{dV} = -\dfrac{P}{V}\), which yields \(B_T = P\). Therefore, the initial…
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