Use the worked example above to help you solve this problem. A balloon contains

Question

Use the worked example above to help you solve this problem. A balloon contains 4.00 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. Find the work Wenv done by the gas in expanding the balloon, the thermal energy Q transferred to the gas, and the work W done on the gas.

Suppose that subsequent to this heating, 1.00 104 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.)

Vf= ______ xVo ******(answer is not 0.458)****

Wenv = 2.23 x 10^3 J (correct answer) Q = 2.23 x 10^3   J (correct answer) W = -2.23 x 10^3   J (correct answer)

Explanation / Answer

given

n = 4 moles

the thermal energy is removed Q = - 1.0 X 104 J

temperature is T = 33 + 273.15

T = 306.15 K

V = 1.25 V0

using equation Q = n R T ln( Vf / V )

-1 X 104 = 4 X 8.314 X 306.15 X ln ( Vf / V )

ln ( Vf / V ) = - 0.9821

Vf / 1.25 V0 = e-0.9821

Vf / 1.25 V0 = 0.3745

Vf = 1.25 X 0.3745 V0

Vf = 0.4681 V0  

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