A certain gas is isothermally compressed to (1/3)rd of its initial volume (Vo = 3 litre) by applying required pressure. If the bulk modulus of the gas is 3 × 10⁵ N/m², the magnitude of work done on the gas is ______ J. Numerical answer type. Work it out, then open the answer.

Answer: 989. For an isothermal process the bulk modulus equals the pressure: B = P, so initial P₀ = 3×10⁵ Pa. Isothermal work: W = P₀V₀ln (V₀)/(Vf) = P₀V₀ln 3 W = 3×10⁵×3×10⁻³×1.0986 = 900×1.0986 W ≈ 989 J

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Bulk Modulus & Compressibility

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\text{rd}}$ of its initial volume $(V_{\text{o}} = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5}\text{ N/m}^2$ , the magnitude of work done on the gas is ______ J.

Numerical answer type. Work it out, then open the answer.

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Answer: 989

For an isothermal process the bulk modulus equals the pressure: $B = P$ , so initial $P_0 = 3\times10^{5}\ \text{Pa}$ .
Isothermal work: $W = P_0V_0\ln\frac{V_0}{V_f} = P_0V_0\ln 3$
$W = 3\times10^{5}\times3\times10^{-3}\times1.0986 = 900\times1.0986$
$W \approx 989\ \text{J}$

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