Plate glass at $600^{\circ} \mathrm{C}$ is cooled by passing air over its surface such that the convection heat transfer coefficient is $h=$ $50 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$. To prevent cracking, it is known that the temperature gradient must not exceed $15^{\circ} \mathrm{C} / \mathrm{mm}$ at any point in the glass during the cooling process. If the thermal conductivity of the glass is $1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$ and its surface emissivity is $0.8$, what is the lowest temperature of the air that can initially be employed for the cooling? Suppose that the temperature of the air equals that of the surroundings.

A $\mathrm{KCl}$ solution containing $42 \mathrm{~g}$ of $\mathrm{KCl}$ per $100 \mathrm{~g}$ of water is cooled from $60{ }^{\circ} \mathrm{C}$ to $0{ }^{\circ} \mathrm{C}$. What happens during cooling?

Use Newton’s law of cooling. [T] You have a cup of coffee at temperature $70^\circ C$ that you put outside, where the ambient temperature is $0^\circ C.$ After 5 minutes, how much colder is the coffee?

A tank of volume $\forall=10 \mathrm{m}^{3}$ contains compressed air at $15^{\circ} \mathrm{C}$. The gage pressure in the tank is 4.50 MPa. Evaluate the work required to fill the tank by compressing air from standard atmosphere conditions for (a) isothermal compression and (b) isentropic compression followed by cooling at constant pressure. What is the peak temperature of the isentropic compression process? Calculate the energy removed during cooling for process (b). Assume ideal gas behavior and reversible processes. Label state points on a Ts diagram and a $p \forall$ diagram for each process.

A mass of 10 g of oxygen fill a weighted piston-cylinder device at 20 kPa and 100$^\circ{}$C. The device is now cooled until the temperature is 0$^\circ{}$C. Determine the change of the volume of the device during this cooling.

With time, $t,$ in minutes, the temperature, $H,$ in degrees Celsius, of a bottle of water put in the refrigerator at $t = 0$ is given by

$$H=4+16e^{-0.02t}.$$

How fast is the water cooling initially? After $10$ minutes? Give units.

What colligative property is*displayed by each of the following situations?

a. Antifreeze is added to a car's cooling system to prevent freezing when the temperature is below $0^{\circ} \mathrm{C}$.

b. Ice melts on sidewalks after salt has been spread on them.

During the process of adiabatic cooling, the temperature decreases because the air has:

a) emitted infrared radiation.

b) lost some of its water vapor.

c) been compressed.

d) expanded to a larger volume.

e) lost heat to the colder air at higher altitudes.

Chloroethane $\left(T_{b p}=-13^{\circ} \mathrm{C}\right)$ has been used as a local anesthetic. When the liquid is sprayed onto the skin, it cools the skin enough to freeze and numb the skin. Explain the cooling effect of this liquid.

$\mathrm{A} \mathrm{KNO}_3$ solution containing $45 \mathrm{~g}$ of $\mathrm{KNO}_3$ per $100 \mathrm{~g}$ of water is cooled from $40^{\circ} \mathrm{C}$ to $0{ }^{\circ} \mathrm{C}$. What happens during cooling?

A dramatic classroom demonstration involves cooling a balloon from room temperature $(298 \mathrm{~K})$ to liquid nitrogen temperature $(77 \mathrm{~K})$. If the initial volume of the balloon is $2.7 \mathrm{~L}$, what will its volume be after it cools?

At the end of its manufacturing process, a silicon wafer of diameter D=150 mm, thickness $\delta=1 \mathrm{mm}$, and $T_{i}=325^{\circ} \mathrm{C}$ and is allowed to cool in quiescent, ambient air and large surroundings for which $T_{\infty}=T_{\mathrm{sur}}=25^{\circ} \mathrm{C}$. (a) What is the initial rate of cooling? (b) How long does it take for the wafer to reach a temperature of $50^{\circ} \mathrm{C}^{\circ}$? Comment on how the relative effects of convection and radiation vary with time during the cooling process.

With time, $t$, in minutes, the temperature, $H$, in degrees Celsius, of a bottle of water put in the refrigerator at $t=0$ is given by

$$H=4+16 e^{-0.02 t} .$$

How fast is the water cooling initially? After ten minutes? Give units.

Draw the cooling curves, including appropriate temperatures, expected for the following A1-Si alloys: (a) $\mathrm{Al}-4 \% \mathrm{Si}$; (b) A1-12.6% $\mathrm{Si}$; (c) $\mathrm{Al}-25 \% \mathrm{Si}$; and (d) Al-65% Si.