I need help with 3A and B. Please show me the detailed steps. For a mole of a perfect monoatomic gas, the internal energy, $ U $, can be expressed as a function of the pressure and volume as\[ U = U(P,V) = \frac{3}{2} PV \]a) Calculate explicitly the line integral of $ dU $ along the closed path $ ABCD $ shown as a black trace in the $ P - V $ graph below.**Graph Explanation:**The graph is a $ P $ (pressure) vs. $ V $ (volume) graph with the following key points:- Point $ A $ at $(V_1, P_1)$- Point $ B $ at $(6V_1, P_1)$- Point $ C $ at $(6V_1, 3P_1)$- Point $ D $ at $(V_1, 3P_1)$The path follows:- From $ A $ to $ B $: Horizontal line at $ P = P_1 $- From $ B $ to $ C $: Vertical line at $ V = 6V_1 $- From $ C $ to $ D $: Horizontal line at $ P = 3P_1 $- From $ D $ to $ A $: Vertical line at $ V = V_1 $b) Compute the following line integrals between the points $ B $ and $ C $ in the figure above:1. $ \int_h PdV $, along the path, $ h $, described by $ P = 3P_1 V_1 / (V - 3V_1) $, shown in red in the figure above.2. $ \int_s PdV $, along the path, $ s $, shown in black in the figure above.Use these results to demonstrate that $ \delta W = -PdV $ is not an exact differential.\[ \text{Problem 3a-3c} \]

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3. For a mole of a perfect monoatomic gas, the internal energy, U, can be expressed as a function of the pressure and volume as 3 U = U(P,V) = PV a) Calculate explicitly the line integral of dU along the closed path ABCD shown as a black trace in the P – V graph below. D C 3P1 2P1 P1 -> A V V1 2V1 3V1 4V1 5V1 6V1 Problem 3a-3c b) Compute the following line integrals between the points B and C in the figure above: 1. S, PdV, along the path, h, described by P = 3P;V/(V – 3V1), shown in red in the figure above. 2. S, PdV, along the path, s, shown in black in the figure above. Use these results to demonstrate that &W = -PdV is not an exact differential. S.

3. For a mole of a perfect monoatomic gas, the internal energy, U, can be expressed as a function of the pressure and volume as 3 U = U(P,V) = PV a) Calculate explicitly the line integral of dU along the closed path ABCD shown as a black trace in the P – V graph below. D C 3P1 2P1 P1 -> A V V1 2V1 3V1 4V1 5V1 6V1 Problem 3a-3c b) Compute the following line integrals between the points B and C in the figure above: 1. S, PdV, along the path, h, described by P = 3P;V/(V – 3V1), shown in red in the figure above. 2. S, PdV, along the path, s, shown in black in the figure above. Use these results to demonstrate that &W = -PdV is not an exact differential. S.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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