Air enters a nozzle operating at steady state at $45\ \mathrm{lbf}$ $/$ in.${ }^2, 800^{\circ} \mathrm{R}$, with a velocity of $480\ \mathrm{ft} / \mathrm{s}$, and expands isentropically to an exit velocity of $1500\ \mathrm{ft} / \mathrm{s}$. Determine (a) the exit pressure, in $\mathrm{lbf} /$ in.$^2$ (b) the ratio of the exit area to the inlet area. (c) whether the nozzle is diverging only, converging only, or converging-diverging in cross section.

An electronic package with a surface area of $1 m^2$ placed in an orbiting space station is exposed to space. The electronics in this package dissipate all 1 kW of its power to the space through its exposed surface. The exposed surface has an emissivity of 1.0 and an absorptivity of 0.25. Determine the steady state exposed surface temperature of the electronic package (a) if the surface is exposed to a solar flux of $750 W/m^2,$ and (b) if the surface is not exposed to the sun.

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.

A mass m is gently placed on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?

For each of the following processes that show the formation of ions, complete the process by indicating the number of electrons that must be gained or lost to form the ion. Indicate the total number of electrons in the ion and in the atom from which it was made.

a. $\mathrm{Al} \rightarrow \mathrm{Al}^{3+}$
b. $\mathrm{S} \rightarrow \mathrm{S}^{2-}$
c. $\mathrm{Cu} \rightarrow \mathrm{Cu}^{+}$
d. $\mathrm{F} \rightarrow \mathrm{F}^{-}$
e. $\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+}$
f. $\mathrm{P} \rightarrow \mathrm{P}^{3-}$

Solve the equation for the indicated variable. $\frac{a x+b}{c x+d}=2;$ for x

Steam enters a counterflow heat exchanger operating at steady state at 0.07 MPa with a specific enthalpy of 2431.6 kJ/kg and exits at the same pressure as saturated liquid. The steam mass flow rate is 1.5 kg/min. A separate stream of air with a mass flow rate of 100 kg/min enters at $30^{\circ}C$ and exits at $60^{\circ}C.$. The ideal gas model with $c_{p}= 1.005 \: kJ/kg \cdot K$ can be assumed for air. Kinetic and potential energy effects are negligible. Determine (a) the quality of the entering steam and (b) the rate of heat transfer between the heat exchanger and its surroundings, in kW.

A plant has the transfer function given by

$$G(s)=\frac{1}{(1+s)(1+0.5 s)}$$

and is controlled by a proportional controller $G_c(s)=K$, as shown in the block diagram in Figure 5.42. The value of $K$ that yields a steady-state error $E(s)=Y(s)-R(s)$ with a magnitude equal to $0.01$ for a unit step input is: a. $K=49$ b. $K=99$ c. $K=169$ d. None of the above In Problems 14 and 15 , consider the control system in Figure 5.42, where

$$G(s)=\frac{6}{(s+5)(s+2)} \text { and } G_c(s)=\frac{K}{s+50}$$

Figure shows a solar collector panel embedded in a roof. The panel, which has a surface area of $24\ \mathrm{ft}^2$, receives energy from the sun at a rate of $200\ \mathrm{Btu} / \mathrm{h}$ per $\mathrm{ft}^2$ of collector surface. Twenty-five percent of the incoming energy is lost to the surroundings. The remaining energy is used to heat domestic hot water from $90$ to $120^{\circ} \mathrm{F}$. The water passes through the solar collector with a negligible pressure drop. Neglecting kinetic and potential effects, determine at steady state how many gallons of water at $120^{\circ} \mathrm{F}$ the collector generates per hour.

Air is compressed in an axial-flow compressor operating at steady state from $27^{\circ} \mathrm{C}, 1$ bar to a pressure of $2.1$ bar. The work input required is $94.6 \mathrm{~kJ}$ per $\mathrm{kg}$ of air flowing through the compressor. Heat transfer from the compressor occurs at the rate of $14 \mathrm{~kJ}$ per kg at a location on the compressor's surface where the temperature is $40^{\circ} \mathrm{C}$. Kinetic and potential energy changes can be ignored. Find

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

(b) the rate at which entropy is produced within the compressor, in $\mathrm{kJ} / \mathrm{K}$ per $\mathrm{kg}$ of air flowing.

Find the standard equation of the sphere. Center: (-3, 2, 4), tangent to the yz-plane

Write a variable expression for each word phrase. 3 divided by n

Find each product. −15(0)

A stainless-steel sphere $\left[k=16 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right]$ having a diameter of $4 \mathrm{~cm}$ is exposed to a convection environment at $20^{\circ} \mathrm{C}, h=15 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$. Heat is generated uniformly in the sphere at the rate of $1.0 \mathrm{MW} / \mathrm{m}^3$. Calculate the steady-state temperature for the center of the sphere.