An electric water heater having a 200-L capacity heats water from $23 \text { to } 55^{\circ} \mathrm{C}.$ Heat transfer from the outside of the water heater is negligible, and the states of the electrical heating element and the tank holding the water do not change significantly. Perform a full exergy accounting, in kJ, of the electricity supplied to the water heater. Model the water as incompressible with a specific heat $c=4.18 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}.$ Let $T_{0}=23^{\circ} \mathrm{C}.$

Determine whether the statement is true or false. Justify your answer. The graph of the function $f(x)=2 x(x-1)^{2}(x+3)^{3}$ touches, but does not cross, the x-axis.

Find the derivatives of the functions. $r(t)=\log _{3}(t+1 / t)$

A spherical balloon filled with helium at 40 $^{\circ} \mathrm{F}$ and 20 psia has a 25- ft diameter. What load can it support in atmospheric air at 40 $^\circ \mathrm{F}$ and 14696 psia? Neglect the balloon's weight.

A gas turbine operating at steady state is shown in figure. Air enters the compressor with a mass flow rate of $5 \mathrm{~kg} / \mathrm{s}$ at $0.95\ \text{bar}$ and $22^{\circ} \mathrm{C}$ and exits at $5.7\ \text{bar}$. The air then passes through a heat exchanger before entering the turbine at $1100 \mathrm{~K}, 5.7\ \text{bar}$. Air exits the turbine at $0.95\ \text{bar}$. The compressor and turbine operate adiabatically and the effects of motion and and gravity can be ignored. The compressor and turbine isentropic efficiencies are $82$ and $85 \%$, respectively. Using the ideal gas model for air, determine, each in $\mathrm{kW}$. (a) the net power developed.

(b) the rates of exergy destruction for the compressor and turbine.

(c) the net rate exergy is carried out of the plant at the turbine exit, $\left(\dot{E_{14}}-\dot{E_{11}}\right)$.

Let $T_0=22^{\circ} \mathrm{C}, p_0=0.95\ \text{bar}$.

A 25-cm-diameter black ball at $130^\circ C$ is suspended in air, and is losing heat to the surrounding air at $25^\circ C$ by convection with a heat transfer coefficient of $12 W/m^2 \cdot K,$ and by radiation to the surrounding surfaces at. $15^\circ C.$ The total rate of heat transfer from the black ball is (a) 217W (b) 247 W (c) 251 W (d) 465 W (e) 2365 W

find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse.

$$4x^2+25y^2+16x-150y+141=0$$

A wood-burning stove (emissivity=0.900 and surface area=3.50 $m^{2}$) is being used to heat a room. The fire keeps the stove surface at a constant $198^{\circ} \mathrm{C}$ (471 K) and the room at a constant $29^{\circ} \mathrm{C}$ (302 K). Determine the net radiant power generated by the stove.

A black wood stove has a surface area of 1.20

$$m^2$$

and a surface temperature of

$$175 ^ { \circ } \mathrm { C }$$

. What is the net rate at which heat is radiated into the room? The room temperature is

$$20 ^ { \circ } \mathrm { C }$$

.

Answer this question with "yes" or "no," and explain your answer - Is PROWESS related to pride?

At Richardson Manufacturing Company, there are two factors that determine the cost of health care. If an employee makes less than $55,000 per year, he pays$40 per month for individual coverage and $85 per month for family coverage. If an employee makes at least$55,000 per year, individual coverage is $70 per month and family coverage is$165 per month. Catherine is a department manager at Richardson. Her annual salary is $68,300. She has family health care. Her employer contributes$935 per month towards her total coverage cost. What percent does Catherine contribute toward the total coverage?

Monisha said that to find det B, where

$$B = \left[ \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right]$$

you can use the expression ad - bc or the expression bc - ad. Is Monisha correct? Explain.

An electron has a constant acceleration of +3.2 m/s$^2$. At a certain instant its velocity is +9.6 m/s. What is its velocity 2.5 s earlier?

Do younger people use Twitter more often than older people? In a random sample of 316 adult Internet users aged 18 to 29, 26% used Twitter. In a separate random sample of 532 adult Internet users aged 30 to 49, 14% used Twitter. Construct and interpret a 90% confidence interval for the difference between the true proportions of adult Internet users in these age groups who use Twitter.