A diatomic ideal gas acts as a heat engine following a process described by the diagram below: Step 1. Isothermal expansion at ThotThot from volume VaVa to a final volume VbVb. The final volume is a factor kk times larger than the initial volume (ie. VbVb=kVakVa).
Step 2. Isobaric contraction from volume VbVb back to original volume VaVa, and cooling from ThotThot to TcTc
Step 3. Isochoric heating returning the system to its original state.

If there are n=82.4mols of the gas, the expansion factor kk=3.2, and initial temperature ThotThot=217.8K, what is the efficiency ee of this cyclic heat engine?

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.