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# CALC A cylinder with a piston contains 0.250 mol of oxygen ISBN: 9780321675460 31

## Solution for problem 64P Chapter 19

University Physics | 13th Edition

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Problem 64P

CALC A cylinder with a piston contains 0.250 mol of oxygen at 2.40 X 105 Pa and 355 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure. (a) Show the series of processes on a pV-diagram. Compute (b) the temperature during the isothermal compression; (c) the maximum pressure; (d) the total work done by the piston on the gas during the series of processes.

Step-by-Step Solution:

Solution 64P Step 1: Here, n = 0.250 mol, Initial pressure is,1P = 2.4 × 10 Pa, Initial temperature is, T = 355 K , 1 The gas then expands isobarically (const pressure) to twice the original volume. This means, V 2 2V wi1h P = P .1 2 We know from ideal gas equation that, PV = nRT ----------(1) V = nR T P Here n, R and P are constant, which means V is directly proportional to the temperature. When the volume gets doubled, temperature also will be doubled. So, T 2 355 × 2 = 710 K . Step 2: The gas then compressed to it’s original volume isothermally (temperature constant). This means, T3= T =2710 K . So, the final temperature after the compression is 710 k. And V =3V . 1 Here first we need to find the initial volume, which can be found by the formula given below. P 1 =1nRT 1 2.4 × 10 × V = 0.250 × 8.314 × 355 1 5 3 V = 10.250 × 8.314 × 355) / (2.4 × 10 ) = 0.00307 = 3.07 × 10 m . Step 3: Then the gas cooled to it’s actual pressure isochorically (const. volume). The maximum pressure is achieved when the gas compressed isothermally to the original volume V . this means the volume gets halved. 1 P maxV /1 = nRT P max = 2nRT = 2 × P = 2 × 2.4 × 10 = 4.8 × 10 Pa. V1 1 The maximum pressure is 4.8 × 10 Pa.5

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##### ISBN: 9780321675460

University Physics was written by and is associated to the ISBN: 9780321675460. This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 64P from 19 chapter was answered, more than 908 students have viewed the full step-by-step answer. This full solution covers the following key subjects: gas, its, original, piston, pressure. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “CALC A cylinder with a piston contains 0.250 mol of oxygen at 2.40 X 105 Pa and 355 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure. (a) Show the series of processes on a pV-diagram. Compute (b) the temperature during the isothermal compression; (c) the maximum pressure; (d) the total work done by the piston on the gas during the series of processes.” is broken down into a number of easy to follow steps, and 95 words. The full step-by-step solution to problem: 64P from chapter: 19 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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