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Get Full Access to University Physics - 13 Edition - Chapter 19 - Problem 3e
Get Full Access to University Physics - 13 Edition - Chapter 19 - Problem 3e

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# CALC Two moles of an ideal gas are compressed in a ISBN: 9780321675460 31

## Solution for problem 3E Chapter 19

University Physics | 13th Edition

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Problem 3E

CALC Two moles of an ideal gas are compressed in a cylinder at a constant temperature of 65.0o C until the original pressure has tripled. (a) Sketch a pV-diagram for this process. (b) Calculate the amount of work done.

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Solution 3E The ideal gas is compressed here and its pressure has tripled. It means that a work is done on the system. (a) The pV diagram can be drawn as shown below. Original pressure of the gas has tripled. This means the volume of the gas will become one third of the initial value. Let. initial pressure P = P 1 Initial volume V = V 1 Final pressure P 2 = 3P P V Final volume V 2= P 1 2 V = PV 2 3P V 2= V /3 (b) The compression of the gas happens at constant temperature. So, this is an isothermal process. V 2 Now, work done in an isothermal process is given by W = nRT dV …..(1), where n is V V 1 the number of moles of the gas, R is the gas constant and T is the absolute temperature. Given that, n = 2 T = 65 C = 273 + 65 K = 338 K Therefore, from equation (1), work done is V 2 W = 2 × 8.314 J/mol.K × 338 K × dV V V 1 V /3 dV W = 2 × 8.314 J/mol.K × 338 K × V V V /3 W = 5620 J × ln V W = 5620 J × ln 3 W = 5620 J × ( 1.1) W = 6182 J Therefore, the amount of work done is 6182 J. The negative sign indicates that work is done on the gas as it is compressed.

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##### ISBN: 9780321675460

This full solution covers the following key subjects: amount, Calc, calculate, compressed, constant. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. Since the solution to 3E from 19 chapter was answered, more than 291 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: University Physics, edition: 13. The full step-by-step solution to problem: 3E from chapter: 19 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. The answer to “CALC Two moles of an ideal gas are compressed in a cylinder at a constant temperature of 65.0o C until the original pressure has tripled. (a) Sketch a pV-diagram for this process. (b) Calculate the amount of work done.” is broken down into a number of easy to follow steps, and 39 words.

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