A well-insulated bucket of negligible heat capacity contains $150 \text{~g}$ of ice at $0^{\circ} \text{C}$. $(b)$ Is any ice left after the system reaches equilibrium?

A $200\text{-g}$ piece of ice at $0^{\circ} \text{C}$ is placed in $500 \text{~g}$ of water at $20^{\circ} \text{C}$. This system is in a container of negligible heat capacity and is insulated from its surroundings. $(b)$ How much of the ice melts?

A $200\text{-g}$ piece of ice at $0^{\circ} \text{C}$ is placed in $500 \text{~g}$ of water at $20^{\circ} \text{C}$. This system is in a container of negligible heat capacity and is insulated from its surroundings. $(a)$ What is the final equilibrium temperature of the system?

Oxygen $\left(\mathrm{O}_2\right)$ is confined to a cubic container $15 \mathrm{~cm}$ on a side at a temperature of $300 \mathrm{~K}$. Compare the average kinetic energy of a molecule of the gas to the change in its gravitational potential energy if it falls from the top of the container to the bottom. "The Distribution of Molecular Speeds

How much heat must be removed when $100 \mathrm{~g}$ of steam at $150^{\circ} \mathrm{C}$ is cooled and frozen into $100 \mathrm{~g}$ of ice at $0^{\circ} \mathrm{C}$ ? (Take the specific heat of steam to be $2.01 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$.)

How much heat is required to convert $10.0 \mathrm{~g}$ of ice at $-5.0^{\circ} \mathrm{C}$ to steam at $100.0^{\circ} \mathrm{C}$ ? The temperaturedependent constant-pressure specific heat capacity of ice is $c_p(T) /\left(\mathrm{kJ} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\right)=1.0187 \mathrm{~T}-1.49 \times 10^{-2}$. The temperature-dependent constant-pressure specific heat for water is $c_p(T) /\left(\mathrm{kJ} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\right)=-1.0 \times$ $10^{-7} T^3+1.0 \times 10^4 T^2-3.92 \times 10^{-2} T+8.7854$.

A $25.0\text{-g}$ glass tumbler contains $200 \text{~mL}$ of water at $24.0^{\circ} \text{C}$. If two $15.0\text{-g}$ ice cubes, each at a temperature of $-3.00^{\circ} \text{C}$, are dropped into the tumbler, what is the final temperature of the drink? Neglect any heat transfer between the tumbler and the room.

During his many appearances at the Tour de France, champion bicyclist Lance Armstrong typically expended an average power of $400 \text{~W}, 5.0$ hours a day for $20$ days. What quantity of water, initially at $24^{\circ} \text{C}$, could be brought to a boil if you could harness all of that energy?

The specific heat of a certain metal can be determined by measuring the temperature change that occurs when a piece of the metal is heated and then placed in an insulated container that is made of the same material and contains water. Suppose the piece of metal has a mass of $100 \text{~g}$ and is initially at $100^{\circ} \text{C}$. The container has a mass of $200 \text{~g}$ and contains $500 \text{~g}$ of water at an initial temperature of $20.0^{\circ} \text{C}$. The final temperature is $21.4^{\circ} \text{C}$. What is the specific heat of the metal?

A gas consists of ions that repel each other. The gas undergoes a free expansion in which no heat is absorbed or released and no work is done. Does the temperature of the gas increase, decrease, or remain the same? Explain your answer.

A 200-g piece of lead is heated to $90^{\circ} \mathrm{C}$ and is then dropped into a calorimeter containing $500 \mathrm{~g}$ of water that is initially at $20^{\circ} \mathrm{C}$. Neglecting the heat capacity of the container, find the final temperature of the lead and water.

While spending the summer on your uncle's horse farm, you spend a week apprenticing with his farrier (a person who makes and fits horseshoes). You observe the way he cools a shoe after pounding the hot, pliable shoe into the correct size and shape. Suppose a $750\text{-g}$ iron horseshoe is taken from the farrier's fire, shaped, and at a temperature of $650^{\circ} \text{C}$, dropped into a $25.0\text{-L}$ bucket of water at $10.0^{\circ} \text{C}$. What is the final temperature of the water after the horseshoe and water arrive at equilibrium? Neglect any heating of the bucket and assume the specific heat of iron is $460 \text{~J} /(\text{kg} \cdot \text{K})$.

A 1400-kg car traveling at $80 \mathrm{~km} / \mathrm{h}$ is brought to rest by applying the brakes. If the specific heat of steel is $0.11 \mathrm{cal} / \mathrm{g} \cdot \mathrm{K}$, what total mass of steel must be contained in the steel brake drums if the temperature of the brake drums is not to rise by more than $120 \mathrm{C}^{\circ}$ ?

You are supervising the creation of some lead castings for use in the construction industry. Each casting involves one of your workers pouring $0.500 \text{~kg}$ of molten lead that has a temperature of $327^{\circ} \text{C}$ into a cavity in a large block of ice at $0^{\circ} \text{C}$. How much liquid water should you plan on draining per hour if there are $100$ workers who are able to each average one casting every $10.0 \text{~min}$?