(Solved): Thermodynamics of Ideal-Gas processes (1.) Explain why the first law of thermodynamics, \( Q+W=\Del ...

Thermodynamics of Ideal-Gas processes (1.) Explain why the first law of thermodynamics, \( Q+W=\Delta E_{t h} \), changes to be \( Q-W_{\text {gas }}= \) \( 3 / 2 N k_{B} \Delta T \) for ideal gases. (2.) The \( p V \) diagram shows two processes, \( A \) and \( B \), that take an ideal gas from the same initial state \( i \) to final state \( f \). (a.) Is more work done by the gas in process \( A \) or in process \( B \) ? Or is the work the same for both? Explain. (b.) Is more heat energy needed for process \( A \) or for process \( B \) ? Or is it the same for both? Explain. Hint: What does having the same initial and final state tell us about the \( \Delta E_{\text {th }} \) of both \( A \) and \( B \) ? (3.) The figure shows an adiabatic expansion of an ideal gas with a constant number of molecules. (a.) The gas's final temperature is lower than its initial temperature. Explain how this can be determined USING JUST THE GRAPH. (b.) How does the figure tell us that positive work is done by the gas? Explain. (c.) Since, by definition, there is no heat involved in this process, what is the only source of energy that the gas could use to do this work? (d.) Use your previous answer to give a physical explanation of why the temperature decreases during an adiabatic expansion.