Under isothermal condition, the pressure of a gas is given by P = a V⁻³, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to (a) P/2 (b) 2 P (c) 3 P (d) P

Answer: (c). B = -VdP/dV dP/dV = -3aV⁻⁴ ⇒ B = 3aV⁻³ = 3P So the answer is (c) 3P.

Under isothermal condition, the pressure of a gas is given by P = a… | JEE Main 2023 (13 Apr, Shift 1)

Q9JEE Main 2023 · 13 APR · SHIFT 1Easy

Bulk Modulus & Compressibility

Under isothermal condition, the pressure of a gas is given by $\text{P} = a\,\text{V}^{-3}$ , where $a$ is a constant and $\text{V}$ is the volume of the gas. The bulk modulus at constant temperature is equal to

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Answer: (c)

$B = -V\dfrac{dP}{dV}$
$\dfrac{dP}{dV} = -3aV^{-4} \Rightarrow B = 3aV^{-3} = 3P$
So the answer is (c) 3P.

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