Show that the Kelvin–Planck and the Clausius expressions of the second law are equivalent.

An inventor claims to have developed a resistance heater that supplies 1.2 kWh of energy to a room for each kWh of electricity it consumes. Is this a reasonable claim, or has the inventor developed a perpetual-motion machine? Explain.

A horizontal water jet impinges against a vertical flat plate at 25 ft/s and splashes off the sides in the vertical plane. If a horizontal force of 350 lbf is required to hold the plate against the water stream, determine the volume flow rate of the water.

Find symmetric equations of the line containing the point $P_{0}$. $P_{0}=(0,0,0)$ and the line is perpendicular to each of the lines $\frac{x+1}{2}=\frac{y-1}{3}=\frac{z}{-2}$ and $\frac{x-3}{3}=\frac{y}{1}=\frac{z+1}{2}$.

What is the Clausius expression of the second law of thermodynamics?

In a refrigerator, heat is transferred from a lower-temperature medium (the refrigerated space) to a higher-temperature one (the kitchen air). Is this a violation of the second law of thermodynamics? Explain.

If the pressure of a substance is increased during a boiling process, will the temperature also increase or will it remain constant? Why?

Can the entropy balance for a closed system be used to prove the Clausius and Kelvin-Planck statements of the second law? Explain.

Define the coefficient of performance of a heat pump in words. Can it be greater than unity?

A heat pump is a device that absorbs energy from the cold outdoor air and transfers it to the warmer indoors. Is this a violation of the second law of thermodynamics? Explain.

What is the Clausius expression of the second law of thermodynamics?

A refrigerator has a COP of 1.5. That is, the refrigerator removes 1.5 kWh of energy from the refrigerated space for each 1 kWh of electricity it consumes. Is this a violation of the first law of thermodynamics? Explain.

A heat pump that is used to heat a house has a COP of 2.5. That is, the heat pump delivers 2.5 kWh of energy to the house for each 1 kWh of electricity it consumes. Is this a violation of the first law of thermodynamics? Explain.

Define the coefficient of performance of a refrigerator in words. Can it be greater than unity?