Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 20 - Entropy and the Second Law of Thermodynamics - Problems - Page 606: 34a

Answer

The gas is monatomic. See explanation

Work Step by Step

Process $D \rightarrow A$ is adiabatic which means the pressure and volume remains the same before and after the process. $p_DV_D^{\gamma} = p_AV_A^{\gamma}$ From the graph we can conclude that $V_D = 8.0V_0$ and $p_D = \frac{p_0}{32}$ and $V_A = V_0$ and $p_A = p_0$ Now we need to know what is the value of $\gamma$ to categorize it in which type of gas it is. Substitute all the values and solve for $\gamma$ $\frac{p_0}{32} 8.0V_0^{\gamma} = p_0V_0^{\gamma}$ $ \frac{8.0V_0^{\gamma}}{V_0^{\gamma} } = \frac{32 p_ 0}{p_0}$ $ 8.0^{\gamma}= 32$ $\gamma = \frac{5}{3}$ From the result, it is known that the gas is monatomic since it has the $\gamma$ value of $\frac{5}{3}$
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