A two-stage compression refrigeration system operates with refrigerant-134a between the pressure limits of 1.4 and 0.10 MPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The refrigerant leaving the low-pressure compressor at 0.4 MPa is also routed to the flash chamber. The vapor in the flash chamber is then compressed to the condenser pressure by the high-pressure compressor, and the liquid is throttled to the evaporator pressure. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the rate of heat removed from the refrigerated space for a mass flow rate of 0.25 kg/s through the condenser, and (c) the coefficient of performance.

A refrigerator uses refrigerant-134a as the working fluid and operates on the vapor-compression refrigeration cycle. The evaporator and condenser pressures are 200 kPa and 1400 kPa, respectively. The isentropic efficiency of the compressor is 88 percent. The refrigerant enters the compressor at a rate of 0.025 kg/s superheated by $10.1^{\circ} \mathrm{C}$ and leaves the condenser subcooled by $4.4^{\circ} \mathrm{C}.$ Determine (a) the rate of cooling provided by the evaporator, the power input, and the COP. Determine (b) the same parameters if the cycle operated on the ideal vapor-compression refrigeration cycle between the same pressure limits.

Air enters the compressor of a Brayton refrigeration cycle at 100 kPa, 270 K. The compressor pressure ratio is 3, and the temperature at the turbine inlet is 315 K. The compressor and turbine have isentropic efficiencies of 82% and 85%, respectively. Determine the a. net work input, per unit mass of air flow, in kJ/kg. b. exergy accounting of the net power input, in kJ per kg of air flowing. Discuss. Let $T_0 = 315K.$

A vapor-compression refrigeration system, using ammonia as the working fluid, has evaporator and condenser pressures of $200$ and $30\ \mathrm{lbf} / \mathrm{in}^2$, respectively. The refrigerant passes through each heat exchanger with a negligible pressure drop. At the inlet and exit of the compressor, the temperatures are $10^{\circ} \mathrm{F}$ and $300^{\circ} \mathrm{F}$, respectively. The heat transfer rate from the working fluid passing through the condenser is $50,000\ \mathrm{Btu} / \mathrm{h}$, and liquid exits at $200\ \mathrm{lbf} / \mathrm{in}^2$, $90^{\circ} \mathrm{F}$. If the compressor operates adiabatically, find (a) the compressor power input, in hp. (b) the coefficient of performance.

A refrigerator uses refrigerant-134a as the working fluid and operates on the ideal vapor-compression refrigeration cycle except for the compression process. The refrigerant enters the evaporator at 120 kPa with a quality of 34 percent

Air enters the compressor of an ideal gas refrigeration cycle at $7^{\circ} \mathrm{C}$ and 35 kPa and the turbine at $37^{\circ} \mathrm{C}$ and 160 kPa. The mass flow rate of air through the cycle is 0.2 kg/s. Assuming variable specific heats for air, determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance.

A refrigerator operates on the ideal vapor-compression refrigeration cycle with R-134a as the working fluid between the pressure limits of 120 and 800 kPa. If the rate of heat removal from the refrigerated space is 32 kJ/s, the mass flow rate of the refrigerant is (a) 0.19 kg/s (b) 0.15 kg/s (c) 0.23 kg/s (d) 0.28 kg/s (e) 0.81 kg/s

An ideal vapor-compression refrigeration cycle is modified to include a counterflow heat exchanger, as shown in figure. Ammonia leaves the evaporator as saturated vapor at $1.0\ \text{bar}$ and is heated at constant pressure to $5^{\circ} \mathrm{C}$ before entering the compressor. Following isentropic compression to $18\ \mathrm{bar}$, the refrigerant passes through the condenser, exiting at $40^{\circ} \mathrm{C}, 18\ \text{bar}$. The liquid then passes through the heat exchanger, entering the expansion valve at $18\ \text{bar}$. If the mass flow rate of refrigerant is $12 \mathrm{~kg} / \mathrm{min}$. determine (a) the refrigeration capacity, in tons of refrigeration. (b) the compressor power input, in $\mathrm{kW}$. (c) the coefficient of performance. Discuss possible advantages and disadvantages of this arrangement.

Estimate the endurance strength of a 1.5-in-diameter rod of AISI 1040 steel having a machined finish and heat-treated to a tensile strength of 110 kpsi, loaded in rotating bending.

Education reform is one of the most hotly debated subjects on both state and national policy makers' list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio in $\%$, (2) TSAL is the average teacher's salary in $\$ 1,000 \mathrm{~s}$, (3) $\mathrm{NC}$ is the median household income in $\$ 1,000$ s, and (4) SGL is the percentage of single-parent households. A portion of the data is shown in the accompanying table.

The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions (“Experimental Measurement of the Stopping Performance of a Tractor-Semitrailer from Multiple Speeds,” NHTSA, DOT HS 811 488, June 2011):

$$\begin{matrix} \text{32.1} & \text{30.6} & \text{31.4} & \text{30.4} & \text{31.0} & \text{31.9}\\ \end{matrix}$$

The cited report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed. Determine the probability of a type II error when $\alpha= .01, \sigma=.65$, and the actual value of m is 31. Repeat this for $\mu=32$.

A spring-mass-damper system, as shown in Figure , is used as a shock absorber for a large high-performance motorcycle. The original parameters selected are $m=1 \mathrm{~kg}, b=9 \mathrm{~N} \mathrm{~s} / \mathrm{m}$, and $k=20 \mathrm{~N} / \mathrm{m}$. (a) Determine the system matrix, the characteristic roots, and the transition matrix $\boldsymbol{\Phi}(t)$. The harsh initial conditions are assumed to be $y(0)=1$ and $d y /\left.d t\right|_{t=0}=2$. (b) Plot the response of $y(t)$ and $y(t)$ for the first two seconds. (c) Redesign the shock absorber by changing the spring constant and the damping constant in order to reduce the effect of a high rate of acceleration force $\dot{y}(t)$ on the rider. The mass must remain constant at $1 \mathrm{~kg}$.

Identify the slope and y-intercept of the line with the given equation. Use the slope and y-intercept to graph the equation. 2x - 3y = 0

Performance data for a pump are

$$\begin{matrix} \text{H (ft)} & \text{90} & \text{87} & \text{81} & \text{70} & \text{59} & \text{43} & \text{22}\\ \text{Q (cfm)} & \text{0} & \text{50} & \text{100} & \text{150} & \text{200} & \text{250} & \text{300}\\ \end{matrix}$$

The pump is to be used to move water between two open reservoirs with an elevation increase of 24 ft. The connecting pipe system consists of 1750 ft of commercial steel pipe containing two $90^{\circ}$ elbows and an open gate valve. Find the flow rate if we use (a) 8-in., (b) 10-in., and (c) 12-in. (nominal) pipe.