1. Why do sidewalks have gaps in them to help stop breakage? How does this help?

2. Just as no mechanical device can be 100% efficient, no heat engine can transfer 100% of its heat to a single object. Some of the heat energy must be wasted (released into the environment). We have a heat engine that produces 150 J of heat, does 40 J of work, and emits 110 J into another system. What is the efficiency of the heat engine? Show your work.

3. The heat of fusion for water is 3.3 x 10⁵ J/kg. How much heat energy is needed to can 3kg of ice at 0C to water at 0C? Show your work.

4. How much heat energy is needed to change 0.25kg of water at 100C to steam at 100C? Show your work.

5. How much heat does a freezer need to remove from 1kg of water at 40C to make ice at 0C? (You will need to use the specific heat of water to drop the temperature first, before trying to make the phase change!) Show your work.