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An ideal gas undergoes the thermodynamic process shown in the ??PV diagram in the figure. Determine whether each of the values (a) Δ?ΔU, (b) ?W, (c) ?Q for the gas is positive, negative, or zero. (Note that ?W is the work done ??on the gas.) Hint: First use the ideal gas law to find the initial and final temperatures in terms of ?0P0 and ?0V0 and determine if the final temperature is greater than, less than, or equal to the initial temperature.

An ideal gas undergoes the thermodynamic process shown in the ??PV diagram in the figure. Determine whether each of the values (a) Δ?ΔU, (b) ?W, (c) ?Q for the gas is positive, negative, or zero. (Note that ?W is the work done ??on the gas.) Hint: First use the ideal gas law to find the initial and final temperatures in terms of ?0P0 and ?0V0 and determine if the final temperature is greater than, less than, or equal to the initial temperature.

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An ideal gas undergoes the thermodynamic process shown in the ??PV diagram in the figure. Determine whether each of the values (a) Δ?ΔU, (b) ?W, (c) ?Q for the gas is positive, negative, or zero. (Note that ?W is the work done ??on the gas.) Hint: First use the ideal gas law to find the initial and final temperatures in terms of ?0P0 and ?0V0 and determine if the final temperature is greater than, less than, or equal to the initial temperature.

 
(a)
ΔU
A.+
B.-
C.0
 
(b)
W
A.+
B.-
C.0
 
(c)
Q
A.+
B.-
C.0
The image presents a pressure-volume (P-V) diagram, commonly used in thermodynamics to show the relationship between the pressure and volume of a gas. ### Description of the Graph: - **Axes**: - The horizontal axis represents volume (V). - The vertical axis represents pressure (P). - **Key Points on the Graph**: - The point at \(V_0\) and \(P_0\) indicates a specific initial volume and pressure. - The point at \(2V_0\) and \(P_0\) indicates a doubled volume with the same initial pressure. - The point at \(V_0\) and \(2P_0\) marks a state with the initial volume and double the initial pressure. - **Graph Path**: - The graph begins at the high-pressure point, \(V_0, 2P_0\), dropping directly downward to \(V_0, P_0\). - It transitions via a diagonal line sloping downward to the final point, \(2V_0, P_0\). - This path is depicted with a bold arrow indicating the direction of change. ### Explanation: This diagram could represent an isothermal expansion process where the gas expands from an initial state of \(V_0, 2P_0\) to a final state of \(2V_0, P_0\), signifying an increase in volume and a decrease in pressure while moving along an isothermal line. The arrow on the line shows the direction of the process, indicating that pressure decreases as volume increases. This type of graph is essential for understanding thermodynamic processes such as work done by gases, and it helps in visualizing how changes in pressure and volume are related in various contexts.
Transcribed Image Text:The image presents a pressure-volume (P-V) diagram, commonly used in thermodynamics to show the relationship between the pressure and volume of a gas. ### Description of the Graph: - **Axes**: - The horizontal axis represents volume (V). - The vertical axis represents pressure (P). - **Key Points on the Graph**: - The point at \(V_0\) and \(P_0\) indicates a specific initial volume and pressure. - The point at \(2V_0\) and \(P_0\) indicates a doubled volume with the same initial pressure. - The point at \(V_0\) and \(2P_0\) marks a state with the initial volume and double the initial pressure. - **Graph Path**: - The graph begins at the high-pressure point, \(V_0, 2P_0\), dropping directly downward to \(V_0, P_0\). - It transitions via a diagonal line sloping downward to the final point, \(2V_0, P_0\). - This path is depicted with a bold arrow indicating the direction of change. ### Explanation: This diagram could represent an isothermal expansion process where the gas expands from an initial state of \(V_0, 2P_0\) to a final state of \(2V_0, P_0\), signifying an increase in volume and a decrease in pressure while moving along an isothermal line. The arrow on the line shows the direction of the process, indicating that pressure decreases as volume increases. This type of graph is essential for understanding thermodynamic processes such as work done by gases, and it helps in visualizing how changes in pressure and volume are related in various contexts.
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