Air is compressed in an axial-flow compressor operating at steady state from $27^{\circ} \mathrm{C}, 1$ bar to a pressure of $2.1$ bar. The work input required is $94.6 \mathrm{~kJ}$ per $\mathrm{kg}$ of air flowing through the compressor. Heat transfer from the compressor occurs at the rate of $14 \mathrm{~kJ}$ per kg at a location on the compressor's surface where the temperature is $40^{\circ} \mathrm{C}$. Kinetic and potential energy changes can be ignored. Find

(a) the temperature of the air at the exit, in ${ }^{\circ} \mathrm{C}$.

(b) the rate at which entropy is produced within the compressor, in $\mathrm{kJ} / \mathrm{K}$ per $\mathrm{kg}$ of air flowing.

Refrigerant 134a initially at $-36^{\circ} \mathrm{C}$ fills a rigid vessel. The refrigerant is heated until the temperature becomes $25^\circ C$ and the pressure is 1 bar. There is no work during the process. For the refrigerant, determine the heat transfer per unit mass and the change in specific exergy, each in kJ/kg. Comment. Let $T_{0}=20^{\circ} \mathrm{C}, p_{0}=0.1 \mathrm{MPa}.$

Air is compressed in an axial-flow compressor operating at steady state from $27^{\circ} \mathrm{C},$ 1 bar to a pressure of 2.1 bar. The work required is 94.6 kJ per kg of air flowing. Heat transfer from the compressor occurs at an average surface temperature of $40^{\circ} \mathrm{C}$ at the rate of 14 kJ per kg of air flowing. The effects of motion and gravity can be ignored. Let $T_{0}=20^{\circ} \mathrm{C}, p_{0}=1$ bar. Assuming ideal gas behavior, (a) determine the temperature of the air at the exit, in $^\circ C,$ (b) determine the rate of exergy destruction within the compressor, in kJ per kg of air flowing, and (c) perform a full exergy accounting, in kJ per kg of air flowing, based on work input.

One kilogram of Refrigerant 134a contained within a piston-cylinder assembly undergoes a process from a state where the pressure is 7 bar and the quality is $50 \%$ to a state where the temperature is $16^{\circ} \mathrm{C}$ and the refrigerant is saturated liquid. Find the change in specific entropy of the refrigerant, in $\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}$. Can this process be accomplished adiabatically?

A closed, rigid tank contains Refrigerant 134a, initially at $100^{\circ} \mathrm{C}$. The refrigerant is cooled until it becomes saturated vapor at $20^{\circ} \mathrm{C}$. For the refrigerant, determine the initial and final pressures, each in bar, and the heat transfer, in kJ/kg. Kinetic and potential energy effects can be ignored.

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 $T_{0}=23^{\circ} \mathrm{C}.$

Air enters a compressor operating at steady state at 1 bar, $22^{\circ} \mathrm{C}$ with a volumetric flow rate of $1 \mathrm{~m}^3 / \mathrm{min}$ and is compressed to $4 \mathrm{bar}, 177^{\circ} \mathrm{C}$. The power input is $3.5 \mathrm{~kW}$. Employing the ideal gas model and ignoring kinetic and potential energy effects, obtain the following results:

(a) For a control volume enclosing the compressor only, determine the heat transfer rate, in $\mathrm{kW}$, and the change in specific entropy from inlet to exit, in $\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}$. What additional information would be required to evaluate the rate of entropy production?

(b) Compute the rate of entropy production, in $\mathrm{kW} / \mathrm{K}$, for an enlarged control volume enclosing the compressor and a portion of its immediate surroundings so that heat transfer occurs at the ambient temperature, $22^{\circ} \mathrm{C}$.

Calculate the total amount of $\alpha$ and $\beta$ and the amount of each microconstituent in a $\mathrm{Pb}-50 \% \mathrm{Sn}$ alloy at $182^{\circ} \mathrm{C}$. What fraction of the total $\alpha$ in the alloy is contained in the eutectic microconstituent?

An Al-Si alloy contains $15 \%$ primary $\beta$ and $85 \%$ eutectic microconstituent immediately after the eutectic reaction has been completed. Determine the composition of the alloy. (See Figure 11-19.)

A Pb-Sn alloy contains $45 \% \alpha$ and $55 \%$ $\beta$ at $100^{\circ} \mathrm{C}$. Determine the composition of the alloy. Is the alloy hypoeutectic or hypereutectic?

Consider an $\mathrm{Al}$-$4 \% ~\mathrm{Si}$ alloy (Figure 11-19). Determine (a) if the alloy is hypoeutectic or hypereutectic; (b) the composition of the first solid to form during solidification; (c) the amounts and compositions of each phase at $578^{\circ} \mathrm{C}$; (d) the amounts and compositions of each phase at $576^{\circ} \mathrm{C}$, the amounts and compositions of each microconstituent at $576^{\circ} \mathrm{C}$; and (e) the amounts and compositions of each phase at $25^{\circ} \mathrm{C}$.

An Al-Si alloy contains $85 \% \alpha$ and $15 \%$ $\beta$ at $500^{\circ} \mathrm{C}$. Determine the composition of the alloy. Is the alloy hypoeutectic or hypereutectic? (See Figure 11-19.)

Consider the Al-Si phase diagram. What are the percentages of the $\alpha$-phase and liquid for an Al-$5$ wt $\%$ Si alloy at $620$ , $600$ , and $578$ $^{\circ} \mathrm{C}$ ? What are the percentages of $\alpha$ and $\beta$ phases in this alloy for an Al-$5$ wt $\%$ Si alloy at $576$ and $550$ $^{\circ} \mathrm{C}$ ?

Determine the phases that are present and the compositions for each phase in $\mathrm{Cu}$-$85$ $\mathrm{wt} \% \mathrm{Ag}$ at $800^{\circ} \mathrm{C}$.