A gas undergoes a process in which the pressure and volume are related by VPn = constant. The bulk modulus of the gas is :
Correct answer: C. P/n
- A. nP
- B. P1/n
- C. P/n
- D. Pn
Explanation
The bulk modulus (B) of a gas is defined as the negative of the volume change ratio to the pressure change, given by B = -V(dp/dV). For processes where VPn = constant, we differentiate this equation to find that dp/dV = -nP/V. Substituting this into the formula for bulk modulus, we find B = P/n. The other options do not fit this derivation:VPⁿ = (V + ΔV)(P + ΔP)ⁿVPⁿ = VPⁿ (1 + ΔV/V)(1 + nΔP/P)∴ ΔV/V = -n ΔP/PK = - ΔP / (ΔV/V) = P/nOption A (nP): This form is unrelated to the bulk modulus expression.Option B (P1/n): This does not match the derived formula for the bulk modulus.Option D (Pn): This option confuses the multiplication of P and n with their division.
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