Exam 22: Heat Engines, Entropy, and the Second Law of Thermodynamics

100 grams of molten lead (600°C) is used to make musket balls. If the lead shot is allowed to cool to room temperature (21°C), what is the change in entropy (in J/K) of the lead? (For the specific heat of molten and solid lead use 1.29 J/g⋅°C; the latent heat of fusion and the melting point of lead are 2.45 × 10⁴ J/kg and 327°C.)

A violation of the second law of thermodynamics would occur if

An automobile engine operates with an overall efficiency of 12%. How much energy is delivered as waste heat (in gallons of gasoline) for each 10 gallons of fuel burned?

An adiabatic free expansion of a gas in a thermally isolated container is not reversible because

A heat engine absorbs 2 500 J of heat from a hot reservoir and expels 1 000 J to a cold reservoir. When it is run in reverse, with the same reservoirs, the engine pumps 2 500 J of heat to the hot reservoir, requiring 1 500 J of work to do so. Find the ratio of the work done by the heat engine to the work done by the pump. Is the heat engine reversible?

The thermal efficiency of a heat engine is given by

Every second at Niagara Falls, some 5000 m³ of water falls a distance of 50 m. What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

Determine the change in entropy (in J/K) when 5.00 moles of an ideal gas at 0°C are compressed isothermally from an initial volume of 100 cm³ to a final volume of 20 cm³.

One end of a copper rod is in thermal contact with a hot reservoir at T = 500 K and the other end is in thermal contact with a cooler reservoir at T = 300 K. Find the entropy change of each reservoir, and the total entropy change, when 8 000 J of heat energy are conducted from one end of the rod to the other with no change in the temperature distribution in the rod.

In a nuclear power plant, the reactor produces 500°C steam that is used to power the steam turbines which generate 1 500 MW of electrical power. The cooling tower eliminates the waste heat at 50°C. If the efficiency of the plant were that of a Carnot engine, at what rate would waste heat be vented to the atmosphere?

For a gas of N identical molecules of molecular volume V_m in total volume V at temperature T, the number of ways of locating the N molecules in the volume is

A 4.00-liter container is divided into two equal parts, one part containing 0.0100 mole of neon, and the other part containing 0.0100 mole of helium. The divider is removed and the gases mix. What is the change in entropy (in J/K) of this system?

A homeowner has a new oil furnace which has an efficiency of 60%. For every 100 barrels of oil needed to heat his house, how much (in barrels of oil) goes up the chimney as waste heat?

The reason that we can calculate the change in entropy of a system is that

A company that produces pulsed gas heaters claims their efficiency is approximately 90%. If an engine operates between 250°C and 25°C, what is its maximum thermodynamic efficiency?

A new electric power plant has an efficiency of 42%. For every 100 barrels of oil needed to run the turbine, how many are essentially lost as waste heat (in barrels of oil) to the environment?

A Carnot cycle, operating as a heat engine, consists, in the order given, of

A steam engine is operating at its theoretical maximum efficiency of 60%. If the waste heat has a temperature of 100°F (38°C), what is the temperature of the boiler?

A vessel containing 10 kg of water is left out where it evaporates. If the temperature remains constant at 20°C, what is the change in entropy (in kcal/K)? (The latent heat of vaporization at 20°C is 585 cal/g.)

A gasoline engine absorbs 2 500 J of heat at 250°C and expels 2 000 J at a temperature of 50°C. The magnitude of the change in entropy (in J/K) for the system is