An ideal gas in a balloon is kept in thermal equilibrium with its constant-tempe

Question

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 8 times its original size? The balloon initially has a pressure of 330 Pa and a volume of 0.9 m3. The ideal gas constant is R = 8.314 J/mol · K.

A. 7.8 J

B. 2400 J

C. 620 J

D. 650 J

Please specify the correct answer choice at the bottom! Also, please show all work and do not present an answer that is not one of the choices! Thank you!

Explanation / Answer

Work done W = nRT ln( V ' / V )

Where V ' = final volume = 8 V

            V = Initial volume

From ideal gas equation , PV = nRT

So, work done W = PV ln( V ' / V )

                           = 330 Pa x 0.9 m 3 x ln( 8V / V )

                           = 297 x ln (8)

                           = 617.6 J

                            ~ 620 J

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