1)A balloon contains 5.50 moles of a monatomic ideal gas. As energy is added to

Question

1)A balloon contains 5.50 moles of a monatomic ideal gas. As energy is added to the system by heat (say, by absorption from the Sun), the volume increases by 25% at a constant temperature of 33.0°C.

2)Suppose that subsequent to this heating, 1.80 10^4 J of thermal energy is removed from the gas isothermally. Find the final volume in terms of the initial volume of the example, V0. (Hint: Follow the same steps as in the example, but in reverse. Use the values in the Practice It section. Also note that the initial volume in this exercise is 1.25 V0.)

I only need help with the 2nd portion of the question. Thank you!!

Explanation / Answer

Thermal energy removed Q = -1.8 x 10 4 J    Since heat removed is taken as negative. No.of moles n = 5.5 mol Temperature T = 33 o C                        = 33 + 273                        = 306 K Initial volume V = 1.25 V o We know Q = nRT ln (V ' / V ) -1.8 x 10 4 J = 5.5 x 8.314 x 306 ln ( V ' / 1.25 V o ) ln( V ' / 1.25 V o ) = -1.286      V ' / 1.25 V o = e -1.286                             = 0.2762                       V ' = 0.2762 x 1.25 V o                            = 0.3453 V o Final volume V ' = 0.3453 V o                             = 0.2762                       V ' = 0.2762 x 1.25 V o                            = 0.3453 V o Final volume V ' = 0.3453 V o

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