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: 8

Answer

a) Equal. b) Greater than.

Work Step by Step

a) We know, for an ideal gas, that $$\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$$ So if the gas starts from point 1 and ends at point 2, no matter what the process is, then the temperature at point 1 $T_1$ is constant and the temperature at point 2 $T_2$ is also constant. Thus, the two processes' temperature differences are the same $$\boxed{\Delta T_A=\Delta T_B}$$ b) Since the temperature change is the same in both cases, the thermal energy change is also the same in both cases. $$\Delta E_{th,A}=\Delta E_{th,B}$$ Hence, $$Q_A+W_A=Q_B+W_B$$ We know that the work done on the gas is given by the area under the curve. $$W=-\rm Area\;under\;the \;curve$$ And we can see that the area under the curve A is greater than that under B. Thus, $ W_A \gt W_B $, and hence the work done on A is more negative than the work done on B, which means that $W_B-W_A \gt 0$ Thus, $$W_B-W_A=Q_A-Q_B\gt 0$$ So, $$Q_A-Q_B\gt 0$$ $$\boxed{Q_A\gt Q_B}$$
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