Consider an engine in which the working substance is $1.23$ mol of an ideal gas for which $_{\gamma}=1.41^{\gamma}=1.41$ The engine runs reversibly in the cycle shown on the $p V$ diagram (Figure 15-23). The cycle consists of an isobaric (constant-pressure) expansion $a$ at a pressure of $15.0$ atm, during which the temperature of the gas increases from 300 to $600 \mathrm{~K}$, followed by an isothermal expansion $b$ until its pressure becomes $3.00$ atm. Next is an isobaric compression $c$ at a pressure of $3.00$ atm, during which the temperature decreases from 600 to $300 \mathrm{~K}$, followed by an isothermal compression $d$ until its pressure returns to 15 atm. Find the work done by the gas, the heat absorbed by the gas, the internal energy change, and the entropy change of the gas, first for each part of the cycle and then for the complete cycle.