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# Nitrogen gas in an expandable container is cooled from ## Problem 52P Chapter 19

University Physics | 13th Edition

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Problem 52P

Nitrogen gas in an expandable container is cooled from 50.0o C to 10.0o C with the pressure held constant at 3.00 X 105 Pa. The total heat liberated by the gas is 2.50 X 104 J. Assume that the gas may be treated as ideal. Find (a) the number of moles of gas; (b) the change in internal energy of the gas; (c) the work done by the gas. (d) How much heat would be liberated by the gas for the same temperature change if the volume were constant?

Step-by-Step Solution:

Solution 52P Problem (a) To find number of moles n Step 1: Initial Temperature of the gas T 1 = 50°C Final Temperature of the gas T 2 = 10°C Change in temperature dT = T - T2 1 = -40°C Constant pressure applied P = 3.00 x 10 Pa The total heat liberated by the gas Q = -2.50 x 10 J (Heat flows out of the gas) Step 2: For constant pressure Heat Liberated Q = nC dT P C P - Heat capacity at constant pressure, for Diatomic Nitrogen Gas C = R P 2 R - gas constant and value is 8.314 J/mol.K Step 3: Rearranging the above equation Q n = C .dT P Finally 2Q n = 7R.dT Step 4: 4 n = 2*(2.* 10 ) 7*8.3*4 (40) n = 21.48 mol number of moles n is 21.48 mol Problem (b) To find change in internal energy dU Step 1: dU = nRdT (no of degrees of freedom of nitrogen molecule is 5) 2 dU = 5 21.48 8.314 ( 40) 2 * * * 4 dU = -17.86 KJ or -1.79x 10 J 4 The change in internal energy dU is -1.79x 10 J Problem (c) To find the work done by the gas Step 1: W = Q - dU 4 4 W = -2.50 x 10 - (-1.79x 10 ) W = -2.50 x 10 + 1.79x 10 4 W = -7.1 x 10 J 3 The work done by the gas is -7.1 x 10 J Problem (d) Step 1: To find the heat liberated by the gas at constant volume Heat liberated Q = nC dT V 5 C V = R2

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##### ISBN: 9780321675460

Since the solution to 52P from 19 chapter was answered, more than 1634 students have viewed the full step-by-step answer. This full solution covers the following key subjects: gas, constant, liberated, heat, change. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “Nitrogen gas in an expandable container is cooled from 50.0o C to 10.0o C with the pressure held constant at 3.00 X 105 Pa. The total heat liberated by the gas is 2.50 X 104 J. Assume that the gas may be treated as ideal. Find (a) the number of moles of gas; (b) the change in internal energy of the gas; (c) the work done by the gas. (d) How much heat would be liberated by the gas for the same temperature change if the volume were constant?” is broken down into a number of easy to follow steps, and 89 words. This textbook survival guide was created for the textbook: University Physics, edition: 13. The full step-by-step solution to problem: 52P from chapter: 19 was answered by Patricia, our top Physics solution expert on 05/06/17, 06:07PM. University Physics was written by Patricia and is associated to the ISBN: 9780321675460.

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