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69. A Carnot engine employs 1.5 mol of nitrogen gas as a working substance, which is...

69. A Carnot engine employs 1.5 mol of nitrogen gas as a working substance, which is considered as an ideal diatomic gas with γ =7.5 at the working temperatures of the engine. The Carnot cycle goes in the cycle ABCDA with AB being an isothermal expansion. The volume at points A and C of the cycle are 5.0×10−3 m3 and 0.15 L, respectively. The engine operates between two thermal baths of temperature 500 K and 300 K. (a) Find the values of volume at B and D.

This is the question copied directly out of the textbook and I am extremely confused on the information that they give. For instance, since nitrogen gas is diatomic, wouldn't γ = 7/5 instead of 7.5? Also, if a Carnot engine expands for its first two phases, then how is it possible that the volume at point C smaller than the volume at point A? That doesn't seem right. I am doing problems to study for a test, and so I was wondering if the textbook's information is incorrect or if I am just completely missing something. I just don't know where to start. Thanks!

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Answer #1

Consider the P-V diagram as shown below 8 V-0.15L-0.15x10-3 m3 v 5.0x10-3 m3 For ideal gas, 7-1 7-1 T P V. 500 (5x10-33 300 5 x10 ( 1.667 ) = 1.39×10-3 m3 500 300 (0.15×10-3 0.15×10-3 з = (1.667) , = 0.54× 10-3 m 3 -0.54L

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