Describe how a heat engine works, including the four strokes of the heat-engine cycle.

Suppose a Carnot engine can be operated between two reservoirs as either a heat engine or a refrigerator. How is the coefficient of performance of the refrigerator related to the efficiency of the heat engine?

Why is the efficiency of a Carnot heat engine the upper bound to the efficiency of an internal combustion engine?

The following nucleus is observed to decay by emitting an $\alpha$ particle: ${ }_{84}^{212} \mathrm{Po}$. Write out the decay process for this nucleus, and determine the energy released in the reaction. Be sure to take into account the mass of the electron associated with the neutral atom.

Mike makes Y dollars per year. His company offers a matching retirement plan in which they agree to match M percent of his contributions up to P percent of his salary. Write an algebraic expression for the maximum value of the employer’s matching contribution.

How are these three terms related? How are they different? a. automated teller machine b. debit card c. stored-value card

Suppose a Carnot engine can be operated between two reservoirs as either a heat engine or a refrigerator. How is the coefficient of performance of the refrigerator related to the efficiency of the heat engine?

The compression ratio r of an engine is the ratio of maximum to minimum gas volume. (For the gasoline engine of the preceding problem, The given figure shows that the compression ratio is 5.) Find a general expression for the engine efficiency of an Otto-cycle engine as a function of compression ratio.

What is the engine piston displacement in liters of an engine whose displacement is listed as

$$450 in.^3?$$

A Carnot engine operates between two heat reservoirs at temperatures $T_{H}$ and $T_{C}$. An inventor proposes to increase the efficiency by running one engine between T and an intermediate temperature T and a second engine between T and $T_{C}$, using as input the heat expelled by the first engine. Compute the efficiency of this composite system, and compare it to that of the original engine.

Reread all or part of the text to help you answer the following questions.

What is the daily routine of the automated house?

The following nucleus is observed to decay by emitting a $\beta^{-}$ particle: ${ }_{16}^{35} \mathrm{~S}$. Write out the decay process for this nucleus, and determine the energy released in the reaction. Be sure to take into account the mass of the electron associated with the neutral atom.

What are some areas that require estimates to record transactions under the matching rule?

Why should the efficiency of any reversible heat engine not exceed that of a Carnot’s engine operating between the highest and lowest temperature of the engine in question? Prove this result mathematically.