Refrigerant 134a enters a compressor operating at a steady state as saturated vapor at $-4^{\circ} \mathrm{C}$ and exits at a pressure of 14 bar. The isentropic compressor efficiency is $75 \%$. Heat transfer between the compressor and its surroundings can be ignored. Kinetic and potential energy effects are also negligible. Find

(a) the exit temperature, in ${ }^{\circ} \mathrm{C}$.

(b) the work input, in $\mathrm{kJ}$ per $\mathrm{kg}$ of refrigerant flowing.

Perform the indicated operation. Then simplify :

$$8 \div 2 \frac{2}{3}$$

Perform the indicated operation and write the result in standard form.

$$\sqrt { - 81 } - \sqrt { - 144 }$$

Perform the indicated operation and, if possible, simplify.

$$\frac{a}{6 a-9 b}-\frac{b}{4 a-6 b}$$

Refrigerant-134a enters a compressor at 180 kPa as a saturated vapor with a flow rate of $0.35 m^3/min$ and leaves at 700 kPa. The power supplied to the refrigerant during compression process is 2.35 kW. What is the temperature of R-134a at the exit of the compressor?

A pin fin of uniform, cross-sectional area is fabricated of an aluminum alloy $(k=160 \mathrm{W} / \mathrm{m} \cdot \mathrm{K})$. The fin diameter is D=4 mm, and the fin is exposed to convective conditions characterized by $h=220 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$. It is reported that the fin efficiency is $\eta_{f}=0.65$. Determine the fin length L and the fin effectiveness $\varepsilon_{f}$. Account for tip convection.

Perform the indicated operation

$$\left(w^6-w^3\right)-\left(-w^2+w\right)$$

Answer the following questions.

(a) On May 1, 2012, Goldberg Company sold some machinery to Newlin Company on an installment contract basis. The contract required five equal annual payments, with the first payment due on May 1, 2012. What present value concept is appropriate for this situation?

(b) On June 1, 2012, Seymour Inc. purchased a new machine that it does not have to pay for until May 1, 2014. The total payment on May 1, 2014, will include both principal and interest. Assuming interest at a 12% rate, the cost of the machine would be the total payment multiplied by what time value of money concept?

(c) Costner Inc. wishes to know how much money it will have available in 5 years if five equal amounts of $35,000 are invested, with the first amount invested immediately. What interest table is appropriate for this situation?

(d) Jane Hoffman invests in a “jumbo”$200,000, 3-year certificate of deposit at First Wisconsin Bank. What table would be used to determine the amount accumulated at the end of 3 years?

A wind turbine is rotating at $15\ \mathrm{rpm}$ under steady winds flowing through the turbine at a rate of $42,000 \mathrm{~kg} / \mathrm{s}$. The tip velocity of the turbine blade is measured to be $250 \mathrm{~km} / \mathrm{h}$. If $180 \mathrm{~kW}$ power is produced by the turbine, calculate $(a)$ the average velocity of the air and $(b)$ the conversion efficiency of the turbine. Take the density of air to be $1.31 \mathrm{~kg} / \mathrm{m}^3$.

An electrically driven pump operating at steady state draws water from a pond at a pressure of 1 bar and a rate of 50 kg/s and delivers the water at a pressure of 4 bar. There is no significant heat transfer with the surroundings, and changes in kinetic and potential energy can be neglected. The isentropic pump efficiency is 75%. Evaluating electricity at 8.5 cents per $k W \cdot h,$ estimate the hourly cost of running the pump.

From a point on the ground, a balloon was observed to have an angle of elevation of $37^{\circ}$. After the balloon ascended $400 \mathrm{~m}$, it was observed to have an angle of elevation of $56^{\circ}$. Determine the height of the balloon above the ground on the first observation.

A city's population is 1000 and growing at $5\%$ a year.Find a formula for the population at time $t$ years from now assuming that the $5\%$ per year is an:
(i) Annual rate (ii) Continuous annual rate

At fast-food restaurants, the lids for drink cups are made with a small amount of flexibility, so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get frustrated, especially if they end up spilling their drinks. At one restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant's lid supplier claims that the diameter of the large lids follows a normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume that the supplier's claim is true.

What percent of large lids have diameters between 3.95 and 4.05 inches?

3. In the figure below, point Z is the image of point X resulting from successive reflections through parelle! lines, /, and /,. a - 11 Ne ee $\mathscr { A }$ a) Label the distance from X to /, 2 and the distance from ¥ to i, &. Also label the distances from Y to |, and Z to i, in terms of aand b.

p) What is the distance between !, and f, in terms of @ and bb?