JEE Mains · Physics · STD 11 - 11. thermodynamics
Under isothermal condition, the pressure of a gas is given by \(P = aV ^{-3}\), where \(a\) is a constant and \(V\) is the volume of the gas. The bulk modulus at constant temperature is equal to \(..........\,P\)
- A \(0.5\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(B =-\frac{ dP }{ dv / v }\) \(Pv ^3= a\) Differentiating w.r.t to pressure \(v^3+P 3 v^2 \frac{d v}{d P}=0\) \(v=-3 \frac{P d v}{d P}=0\) \(v=-3 \frac{P d v}{d P}\) \(\frac{d P . v}{d v}=-3 P\) \(B=-\left(\frac{d P v}{d v}\right)=-(-3 P)=3 P\)
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