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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
Given: Under isothermal conditions, $$P = aV^{-3}$$ where $$a$$ is a constant.
The bulk modulus at constant temperature is defined as:
$$B = -V \frac{dP}{dV}$$
Differentiate P with respect to V.
$$\frac{dP}{dV} = a \cdot (-3) \cdot V^{-4} = -3aV^{-4}$$
Compute the bulk modulus.
$$B = -V \cdot (-3aV^{-4}) = 3aV^{-3} = 3P$$
Therefore, the correct answer is Option A: $$\mathbf{3P}$$.
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