For full marks you must $...$

Include a conceptual model $($i$.$e$.$ sketch$)$ of the system with the control volume indicated by a dashed

line $($please label it CV$)$ for Problems $1$&$3.$

Define your symbols and show them on your sketch.

Clearly show all unit conversions.

State all assumptions

Clearly state the final answer in a brief sentence.

Where relevant $($Problems $1$a$,1$b$,$ and $3$a$)$ start with the differential form of the energy or mass balance

equation

Problem $1(10$pts$)$: A family needs hot water. They intend to use a solar panel to generate electricity, and then

use the electricity to power a water heater. Some of the incoming solar energy is converted to electricity, while

some is released as heat, and some is absorbed by the solar panel. Suppose the solar intensity $($called the solar

insolation$)$ is $875\frac{W}{m^2}.$ The internal components of the solar panel absorb $75\frac{W}{m^2}($This energy is lost$).$ The

panel efficiency is $24\%("$Efficiency$"$ here is the fraction of incoming energy $-$ from the sun $-$ converted to

electricity$).$

a$)$ How much electricity is generated and how much heat is released at stealy state? Express your answer

in $\frac{W}{m^2}.(5$pts$)$

b$)$ The family needs $170L$ of hot water each day. Assume the water heater is a batch reactor $($for water$)$

and is $100\%$ efficient in energy. How many solar panels are needed to heat the water from $68F$ to

$149F?$ Assume a typical rooftop solar panel is $1\mathrm{.}7m1\mathrm{.}0m,$ and that the panel receives $875\frac{W}{m^2}$ for

six hours. Round your answer to the next integer. $(5$pts$)$