Water at 70 kPa and $100^\circ C$ is compressed isentropically in a closed system to 4 MPa. Determine the final temperature of the water and the work required, in kJ/kg, for this compression.

A piston/cylinder contains air at 600 kPa, 290 K and a volume of 0.01 $m^3$. A constant-pressure process gives 54 kJ of work out. Find the final volume and temperature of the air.

Sketch and find the area of the region R described in terms of the given parametric curves. R is bounded by the x-axis, the hyperbola x = sect, y = tan t , and the ray joining the origin to the point $\left(\sec t_{0}, \tan t_{0}\right)$.

On a $T-s$ diagram, does the actual exit state (state 2) of an adiabatic turbine have to be on the right-hand side of the isentropic exit state (state $2s$)? Why?

In a given location, would a helicopter require more energy in summer or winter to achieve a specified performance? Explain.

Let C(q) represent the cost and R(q) represent the revenue, in dollars, of producing q items. If C'(100)=38 and R'(100)=35, should the company produce the $101^{\mathrm {st }}$ item? Why or why not?

An isentropic steam turbine processes 2 kg/s of steam at 3 MPa, which is exhausted at 50 kPa and $100^\circ C.$ 5 percent of this flow is diverted for feedwater heating at 500 kPa. Determine the power produced by this turbine, in kW.

Money flows continuously into an account beginning at a rate of $5,000 per year and increasing at 10% per year. Interest causes the account to grow at a real rate of 6% (so that$1 grows to $\$ 1.06^{t}$ in t years). How long will it take for the balance in the account to reach $1,000,000?

A bucket is raised vertically from ground level at a constant speed of 2 rn/min by a winch. If the bucket weighs 1 kg and contains 15 kg of water when it starts up but loses water by leakage at a rate of 1 kg/min thereafter, how much work must be done by the winch to raise the bucket to a height of 10 m?

The table shows the approximate population of several countries. Order the countries from the greatest population to the least population.

$$\begin{array}{|l|l|}\hline \text { Country } & {\text { Population }} \\ \hline \text { China } & {1.3 \times 10^{9}} \\ \hline \text { India } & {1.2 \times 10^{9}} \\ \hline \text { Indonesia } & {2.3 \times 10^{8}} \\ \hline \text { United States } & {3.1 \times 10^{8}} \\ \hline\end{array}$$

Find a tangent to the graph of $y=x^{3}+a x^{2}+b x+c$ that is not parallel to any other tangent.

Write the decimal as a fraction or mixed number in simplest form. 5.55

Find the arc length of each curve. $r=f(\theta)=e^{2 \theta}$ from $\theta=0$ to $\theta=2$.

Steam enters an adiabatic diffuser at 150 kPa and $120^\circ C$ with a velocity of 550 m/s. Determine the minimum velocity that the steam can have at the outlet when the outlet pressure is 300 kPa.