I need help with A and B for this problem. I want to see the detailed steps. ### Problem 3a-3c: Internal Energy of a Perfect Monoatomic Gas#### Problem Statement:For a mole of a perfect monoatomic gas, the internal energy \( U \) can be expressed as a function of pressure and volume:\[ U = U(P, V) = \frac{3}{2}PV \]#### Tasks:a) **Calculate the Line Integral of \( dU \):** Calculate explicitly the line integral of \( dU \) along the closed path \( ABCD \) shown as a black trace in the \( P-V \) graph.b) **Compute the Line Integrals Between Points B and C:** 1. \(\int_h PdV\), along the path \( h \), described by \( P = \frac{3P_1V_1}{(V - 3V_1)} \), shown in red in the figure.2. \(\int_s PdV\), along the path \( s \), shown in black.#### Graph Description:- **Axes:** The graph displays a pressure-volume (\( P-V \)) plot.- **Coordinates:** - \( P \): Pressure axis (vertical) - \( V \): Volume axis (horizontal)- **Points:** - \( A \): Starts at \( P_1, V_1 \) - \( B \): Ends at \( P_1, 6V_1 \) - \( C \): At \( 3P_1, 6V_1 \) - \( D \): At \( 3P_1, V_1 \)- **Paths:** - **AB**: Horizontal, from \( A \) to \( B \) - **BC**: Vertical, from \( B \) to \( C \) - **CD**: Horizontal, from \( C \) to \( D \) - **DA**: Ascending diagonally, from \( D \) back to \( A \)The closed cycle \( ABCD \) encompasses these paths.#### Analysis:Use the given functions to calculate the integrals and demonstrate that \( \delta W = -PdV \) is not an exact differential, highlighting the significance in thermodynamics.

Given, The internal energy UUP,V=32PV

Answered: 3. For a mole of a perfect monoatomic…

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