Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 17 - Work, Heat, and the First Law of Thermodynamics - Conceptual Questions - Page 496: 9

Answer

See the detailed answer below.

Work Step by Step

As we see in the given graph, it is a compression-isobaric process. The work done on the gas in this process is given by $$W=-\int_i^f ​PdV=-P( V_f- V_i)$$ where $( V_f-V_i\lt 0)$ is negative since the gas compresses. Thus, the work done on the gas here is positive. $$W=P(V_i-V_f)$$ We know, for an ideal gas, undergoes an isobaric process that $$\dfrac{\color{red}{\bf\not} P_1V_1}{T_1}=\dfrac{\color{red}{\bf\not} P_2V_2}{T_2}$$ Hence, $$\dfrac{V_1}{V_2}=\dfrac{T_1}{T_2}$$ where $V_1\gt V_2$, so $$\dfrac{V_1}{V_2}=\dfrac{T_1}{T_2}\gt 1$$ So, $$T_1\gt T_2$$ This means that during this process we need to decrease the system's temperature. Thus, heat is moved out of our system. This also means that the final thermal energy of the system is less than the initial thermal energy of the system. So, from all the above, $$\boxed{E_{f,th}=E_{i,th}+W-Q}$$ See the bar chart of this equation below. To proceed with this process, we need to: 1- Let the piston moves freely by unlocking the pin. 2- Not changing the mass above the piston to maintain the pressure constant. 3- Put the ice in contact with the bottom of the cylinder. ---
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