An ideal gas in a balloon is kept in thermal equilibrium with its constant-temperature surroundings. How much work is done by the gas if the outside pressure is slowly reduced, allowing the balloon to expand to 6.0 times its original size? The balloon initially has a pressure of 645.0 Pa and a volume of 0.10 m³. The ideal gas constant is R = 8.314 J/mol ∙ K. A) 120 J B) 390 J C) -330 J D) 6.0 J

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Quizplus · Accepted Answer

The work done by the gas is given by the area under the curve on a P-V diagram. Since the pressure is slowly reduced, the process is isothermal and the curve is a hyperbola. The area under the curve is given by the integral of P dV, which is equal to nRT ln(V2/V1), where n is the number of moles of gas, R is the ideal gas constant, T is the temperature, V1 is the initial volume, and V2 is the final volume. Plugging in the given values, we get:W = nRT ln(V2/V1) = (1 mol)(8.314 J/mol ∙ K)(293 K) ln(6) = 390 J

An Ideal Gas in a Balloon Is Kept in Thermal