Question

9. Suppose you place an ice cube in a beaker of room-temperature water, then seal them in a rigid, well-insulated container. No energy can enter or leave the container.

a. If you open the container an hour later, will you find a beaker of water slightly cooler than room temperature, or a large ice cube and some $100°\mathrm{C}$steam?

b. Finding a large ice cube and some $100°\mathrm{C}$steam would not violate the first law of thermodynamics. $W=0\mathrm{J}$and $Q=0\mathrm{J}$because the container is sealed, and $\Delta E_{\text{th}}=0\mathrm{J}$because the increase in thermal energy of the water molecules that became steam is offset by the decrease in thermal energy of the water molecules that turned to ice. Energy would be conserved, yet we never see an outcome like this. Why not?

Short answer

a. The temperature of the water is somewhat cooler than that of the room.

b. It is the 2nd law of thermodynamics that states heat must transfer from hot to cold.

Step-by-step solution

Concept Introduction (Part a)

Thermodynamic equilibrium occurs when two bodies or closed systems are in equilibrium, and in this state only energy can be transferred through partitions permeable to heat, leaving the states of the bodies unchanged.

Explanation (Part a)

(a) Any interaction that involves two systems with different temperatures will reach the thermal equilibrium when their final temperature is the same.

The heat will transfer from the highest energy system to the lowest energy system in the thermal interaction.

This means that as the water loses energy, the temperature becomes less than room temperature.

Final Answer (Part a)

Therefore, water slightly cooler than room temperature.

Concept Introduction (Part b)

Thermodynamic equilibrium occurs when two bodies or closed systems are in equilibrium, and in this state only energy can be transferred through partitions permeable to heat, leaving the states of the bodies unchanged.

Explanation (Part b)

The second law of thermodynamics states that energy must transfer upon the collision of molecules in two different systems.

Therefore, both systems have different energies.

As long as heat transfers from hot to cold, the first law follows this process but cannot see it.

Final Answer (Part b)

Reason: Because 2the nd law states that the heat must transfer from hot to cold.