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.

The hot-water needs of a household are to be met by heating water at $55^{\circ} \mathrm{F}$ to $180^{\circ} \mathrm{F}$ by a parabolic solar collector at a rate of $4 \mathrm{~lbm} / \mathrm{s}$. Water flows through a $1.25$-$\mathrm{in}$-diameter thin aluminum tube whose outer surface is black-anodized in order to maximize its solar absorption ability. The centerline of the tube coincides with the focal line of the collector, and a glass sleeve is placed outside the tube to minimize the heat losses. If solar energy is transferred to water at a net rate of $400 \mathrm{~Btu} / \mathrm{h}$ per $\mathrm{ft}$ length of the tube, determine the required length of the parabolic collector to meet the hot-water requirements of this house.

Compare the potential energy represented by 1 lb of water vapor at $59^{\circ} \mathrm{F}\left(15^{\circ} \mathrm{C}\right)$ and an elevation of 5,000 ft to the energy that would be released when it condenses into rain (1 Btu = 778 ft-lb).

Air expands through a turbine from 8 bar, 960 K to 1 bar, 450 K. The inlet velocity is small compared to the exit velocity of 90 m/s. The turbine operates at steady state and develops a power output of 2500 kW. Heat transfer between the turbine and its surroundings and potential energy effects are negligible. Modeling air as an ideal gas, calculate the mass flow rate of air, in kg/s, and the exit area, in $m^2$. .

As sketched in figure, a condenser using river water to condense steam with a mass flow rate of $2 \times 10^5 \mathrm{~kg} / \mathrm{h}$ from saturated vapor to saturated liquid at a pressure of $0.1\ \text{bar}$ is proposed for an industrial plant. Measurements indicate that several hundred meters upstream of the plant, the river has a volumetric flow rate of $2 \times 10^5 \mathrm{~m}^3 / \mathrm{h}$ and a temperature of $15^{\circ} \mathrm{C}$. For operation at steady state and ignoring changes in kinetic and potential energy, determine the river-water temperature rise, in ${ }^{\circ} \mathrm{C}$, downstream of the plant traceable to use of such a condenser, and comment.

The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation $\sigma= 20 hours.$ A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. (a) Is there evidence to support the claim that mean life exceeds 540 hours? Use a fixed-level test with $\alpha = 0.05.$ (b) What is the P-value for this test? (c) What is the $\beta-value$ for this test if the true mean life is 560 hours? (d) What sample size would be required to ensure that $\beta$ does not exceed 0.10 if the true mean life is 560 hours? (e) Construct a 95% one-sided lower CI on the mean life. (f) Use the CI found in part (e) to test the hypothesis.

As shown in figure, air enters a pipe at $25^{\circ} \mathrm{C}, 100\ \mathrm{kPa}$ with a volumetric flow rate of $23 \mathrm{~m}^3 / \mathrm{h}$. On the outer pipe surface is an electrical resistor covered with insulation. With a voltage of $120 \mathrm{~V}$, the resistor draws a current of 4 amps. Assuming the ideal gas model with $c_p=1.005 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$ for air and ignoring kinetic and potential energy effects, determine (a) the mass flow rate of the air, in $\mathrm{kg} / \mathrm{h}$, and $(\mathrm{b})$ the temperature of the air at exit, in ${ }^{\circ} \mathrm{C}$.

Refrigerant $134 \mathrm{a}$ enters a heat exchanger at $-12^{\circ} \mathrm{C}$ and a quality of $42 \%$ and exits as saturated vapor at the same temperature with a volumetric flow rate of $0.85 \mathrm{~m}^3 / \mathrm{min}$. A separate stream of air enters at $22^{\circ} \mathrm{C}$ with a mass flow rate of $188 \mathrm{~kg} / \mathrm{min}$ and exits at $17^{\circ} \mathrm{C}$. Assuming the ideal gas model for air and ignoring kinetic and potential energy effects, determine (a) the mass flow rate of the Refrigerant $134 \mathrm{a}$, in $\mathrm{kg} / \mathrm{min}$, and (b) the heat transfer between the heat exchanger and its surroundings, in $\mathrm{kJ} / \mathrm{min}$.

Steam enters a heat exchanger operating at steady state at $250\ \mathrm{kPa}$ and a quality of $90 \%$ and exits as saturated liquid at the same pressure. A separate stream of oil with a mass flow rate of $29 \mathrm{~kg} / \mathrm{s}$ enters at $20^{\circ} \mathrm{C}$ and exits at $100^{\circ} \mathrm{C}$ with no significant change in pressure. The specific heat of the oil is $c=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$. Kinetic and potential energy effects are negligible. If heat transfer from the heat exchanger to its surroundings is $10 \%$ of the energy required to increase the temperature of the oil, determine the steam mass flow rate. in $\mathrm{kg} / \mathrm{s}$.

The cooling coil of an air-conditioning system is a heat exchanger in which air passes over tubes through which Refrigerant 22 flows. Air enters with a volumetric flow rate of $40 \mathrm{~m}^3 / \mathrm{min}$ at $27^{\circ} \mathrm{C}, 1.1$ bar, and exits at $15^{\circ} \mathrm{C}, 1$ bar. Refrigerant enters the tubes at 7 bar with a quality of $16 \%$ and exits at 7 bar, $15^{\circ} \mathrm{C}$. Ignoring heat transfer from the outside of the heat exchanger and neglecting kinetic and potential energy effects, determine at steady state (a) the mass flow rate of refrigerant, in $\mathrm{kg} / \mathrm{min}$. (b) the rate of energy transfer, in $\mathrm{kJ} / \mathrm{min}$, from the air to the refrigerant.

Steam at a pressure of $0.08$ bar and a quality of $93.2 \%$ enters a shell-and-tube heat exchanger where it condenses on the outside of tubes through which cooling water flows, exiting as saturated liquid at $0.08$ bar. The mass flow rate of the condensing steam is $3.4 \times 10^5 \mathrm{~kg} / \mathrm{h}$. Cooling water enters the tubes at $15^{\circ} \mathrm{C}$ and exits at $35^{\circ} \mathrm{C}$ with negligible change in pressure. Neglecting stray heat transfer and ignoring kinetic and potential energy effects, determine the mass flow rate of the cooling water, in $\mathrm{kg} / \mathrm{h}$, for steady-state operation.

Oil enters a counterflow heat exchanger at 450 K with a mass flow rate of 10 kg/s and exits at 350 K. A separate stream of liquid water enters at $20^{\circ}C$, 5 bar. Each stream experiences no significant change in pressure. Stray heat transfer with the surroundings of the heat exchanger and kinetic and potential energy effects can be ignored. The specific heat of the oil is constant, $c = 2 \: kJ/kg \cdot K.$ If the designer wants to ensure no water vapor is present in the exiting water stream, what is the allowed range of mass flow rates for the water, in kg/s?

Refrigerant 134a at a flow rate of 0.5 lb/s enters a heat exchanger in a refrigeration system operating at steady state as saturated liquid at $0^{\circ}F$ and exits at $20^{\circ}F$ at a pressure of $20 \: lbf/in.^2$ A separate air stream passes in counterflow to the Refrigerant 134a stream, entering at $120^{\circ}F$ and exiting at $77^{\circ}F$. The outside of the heat exchanger is well insulated. Neglecting kinetic and potential energy effects and modeling the air as an ideal gas, determine the mass flow rate of air, in lb/s.

Ammonia enters a heat exchanger operating at steady state as a superheated vapor at $14\ \text{bar}$, $60^{\circ} \mathrm{C}$, where it is onled and condensed to saturated liquid at 14 bar. The mass flow rate of the ammonia is $450 \mathrm{~kg} / \mathrm{h}$. A separate stream of air enters the heat exchanger at $17^{\circ} \mathrm{C}, 1$ bar and exits at $42^{\circ} \mathrm{C}$, $1\ \text{bar}$. Ignoring heat transfer from the outside of the heat exchanger and neglecting kinetic and potential energy effects, determine the mass flow rate of the air, in $\mathrm{kg} / \mathrm{min}$.