Argon gas enters an adiabatic compressor at 14 psia and 75$^\circ{}$F with a velocity of 60 ft/s, and it exits at 200 psia and 240 ft/s. If the isentropic efficiency of the compressor is 87 percent, determine (a) the exit temperature of the argon and (b) the work input to the compressor.

Consider a Carnot cycle executed in a closed system with air as the working fluid. The maximum pressure in the cycle is 1300 kPa while the maximum temperature is 950 K. If the entropy increase during the isothermal heat rejection process is $0.25 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}$ and the net work output is 100 kJ/kg, determine (a) the minimum pressure in the cycle, (b) the heat rejection from the cycle, and (c) the thermal efficiency of the cycle. (d) If an actual heat engine cycle operates between the same temperature limits and produces 5200 kW of power for an air flow rate of 95 kg/s, determine the second law efficiency of this cycle.

Argon gas enters an adiabatic compressor at 120 kPa and $30^{\circ} \mathrm{C}$ with a velocity of 20 m/s and exits at 1.2 MPa, $530^{\circ} \mathrm{C},$ and 80 m/s. The inlet area of the compressor is $130 \mathrm{cm}^{2}.$ Assuming the surroundings to be at $25^{\circ} \mathrm{C}$, determine the reversible power input and exergy destroyed.

Combustion gases enter an adiabatic gas turbine at 1540$^\circ{}$F and 120 psia and leave at 60 psia with a low velocity. Treating the combustion gases as air and assuming an isentropic efficiency of 82 percent, determine the work output of the turbine. Answer: 717 Btu/lbm

Argon gas enters an adiabatic compressor at 14 psia and $75^{\circ} \mathrm{F}$ with a velocity of 60 ft/s, and it exits at 200 psia and 240 ft/s. If the isentropic efficiency of the compressor is 87 percent, determine (a ) the exit temperature of the argon and (b ) the work input to the compressor.

Helium gas is compressed from 90 kPa and 30$^\circ{}$C to 450 kPa in a reversible, adiabatic process. Determine the final temperature and the work done, assuming the process takes place (a) in a piston-cylinder device and (b) in a steady-flow compressor.

Steam at 3 MPa and 400$^\circ{}$C is expanded to 30 kPa in an adiabatic turbine with an isentropic efficiency of 92 percent. Determine the power produced by this turbine, in kW, when the mass flow rate is 2 kg/s.

Saturated refrigerant-134a vapor at 15 psia is compressed reversibly in an adiabatic compressor to 80 psia. Determine the work input to the compressor. What would your answer be if the refrigerant were first condensed at constant pressure before it was compressed?

Air at 600 kPa and 500 K enters an adiabatic nozzle that has an inlet-to-exit area ratio of 2:1 with a velocity of 120 m/s and leaves with a velocity of 380 m/s. Determine (a) the exit temperature and (b) the exit pressure of the air. Answers: (a) 437 K, (b) 331 kPa

It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if King Hiero’s crown was actually made of pure gold. While in the bathtub, he conceived the idea that he could determine the average density of an irregularly shaped object by weighing it in air and also in water. If the crown weighed 3.55 kgf (= 34.8 N) in air and 3.25 kgf (= 31.9 N) in water, determine if the crown is made of pure gold. The density of gold is $19,300 kg/m^3$. Discuss how you can solve this problem without weighing the crown in water but by using an ordinary bucket with no calibration for volume. You may weigh anything in air.

Saturated water vapor at 200$^\circ{}$C is condensed to a saturated liquid at 50$^\circ{}$C in a spring-loaded piston-cylinder device. Determine the heat transfer for this process in kJ/kg.

Consider the following concentration-time data for the decomposition reaction $\mathrm{AB} \longrightarrow \mathrm{A}+\mathrm{B}$.

$$\begin{array}{llllll} \hline \text { Time (min) } & 0 & 20 & 40 & 12 & 220 \\ {[\mathrm{AB}]} & 0.206 & 0.186 & 0.181 & 0.117 & 0.036 \\ \hline \end{array}$$

(a) Determine the order of the reaction and the value of the rate constant.
(b) What is the molarity of AB after a reaction time of $192 \mathrm{~min}$?
(c) What is the time (in minutes) when the AB concentration reaches a value of $0.0250 \mathrm{M}$?

Using the expression $d S=\frac{C_P}{T} d T-V \beta d P$, calculate the decrease in temperature that occurs if $2.25\ moles$ of water at $310. \mathrm{K}$ and $1650.\ bar$ is brought to a final pressure of $1.30\ bar$ in a reversible adiabatic process. Assume that $\kappa=0$.

The surface area of a cone (excluding the bottom) is given by $S=\pi r \sqrt{r^2+h^2}$, where $r$ is its radius and $h$ is its height. If the height is twice the radius, write a formula for $S$ in terms of $r$.