A certain gas is isothermally compressed to of its initial volume by applying required pressure. If the bulk modulus

Question

A certain gas is isothermally compressed to ${(\frac{1}{3})}^{rd}$ of its initial volume $(V_{0} = 3 litre)$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5} {N/m}^{2}$ , the magnitude of work done on the gas is _______ J. [2026]

Smart Achievers · Accepted Answer

(989)

$Initial volume (V_{1}) = 3 litre$

$Final volume (V_{2}) = \frac{V_{1}}{3} = 1 litre = 10^{- 3} m^{3}$

$For isothermal process, Bulk modulus = Pressure (B = P)$

$Bulk modulus of gas for isothermal process is not constant.$

$In the given solution we have considered it as initial bulk modulus.$

$For isothermal process work done, W = P_{1} V_{1} \ln (\frac{V_{2}}{V_{1}})$

$W = (3 \times 10^{5}) \times (3 \times 10^{- 3}) \ln (\frac{10^{- 3}}{3 \times 10^{- 3}})$

$W = - 988.75 J = 989 J$

Solution

Q.
A certain gas is isothermally compressed to ${(\frac{1}{3})}^{rd}$ of its initial volume $(V_{0} = 3 litre)$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5} {N/m}^{2}$ , the magnitude of work done on the gas is _______ J. [2026]

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Solution

Q. A certain gas is isothermally compressed to (13)rd of its initial volume (V0=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. [2026]

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Q.
A certain gas is isothermally compressed to ${(\frac{1}{3})}^{rd}$ of its initial volume $(V_{0} = 3 litre)$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5} {N/m}^{2}$ , the magnitude of work done on the gas is _______ J. [2026]