Chapter 19: Work, Heat, and the First Law of Thermodynamics

You need to raise the temperature of a gas by 10°C. To use the least amount of heat energy, should you heat the gas at constant pressure or at constant volume? Explain.

A 2000 cm3 container holds 0.10 mol of helium gas at 300°C. How much work must be done to compress the gas to 1000 cm3 at (a) constant pressure and (b) constant temperature?

The burner on an electric stove has a power output of 2.0 kW. A 750 g stainless steel teakettle is filled with 20°C water and placed on the already hot burner. If it takes 3.0 min for the water to reach a boil, what volume of water, in cm3, was in the kettle? Stainless steel is mostly iron, so you can assume its specific heat is that of iron.

When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist airways. Consequently, an adult human exhales about 25 mg of evaporated water with each breath. Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation is much like boiling, only water’s heat of vaporization at 35°C is a somewhat larger 24 * 105 J/kg because at lower temperatures more energy is required to break the molecular bonds. At 12 breaths/min, on a dry day when the inhaled air has almost no water content, what is the body’s rate of energy loss (in J/s) due to exhaled water? (For comparison, the energy loss from radiation, usually the largest loss on a cool day, is about 100 J/s.)

512 g of an unknown metal at a temperature of 15°C is dropped into a 100 g aluminum container holding 325 g of water at 98°C. A short time later, the container of water and metal stabilizes at a new temperature of 78°C. Identify the metal.

A 150 L 1≈40 gal2 electric hot-water tank has a 5.0 kW heater.

How many minutes will it take to raise the water temperature from 65°F to 140°F?

The specific heat of most solids is nearly constant over a wide temperature range. Not so for diamond. Between 200 K and 600 K,

the specific heat of diamond is reasonably well described by c = 2.8T - 350 J/kg K, where T is in K. For gemstone diamonds, 1 carat = 200 mg. How much heat energy is needed to raise the temperature of a 3.5 carat diamond from -50°C to 250°C?

A lava flow is threatening to engulf a small town. A 400-m-wide, 35-cm-thick tongue of 1200°C lava is advancing at the rate of 1.0 m per minute. The mayor devises a plan to stop the lava in its tracks by flying in large quantities of 20°C water and dousing it. The lava has density 2500 kg/m3, specific heat 1100 J/kg K, melting temperature 800°C, and heat of fusion 4.0 * 105 J/kg. How many liters of water per minute, at a minimum, will be needed to save the town?

Suppose you take and hold a deep breath on a chilly day, inhaling 3.0 L of air at 0°C and 1 atm. a. How much heat must your body supply to warm the air to your internal body temperature of 37°C? b. By how much does the air’s volume increase as it warms?

Your 300 mL cup of coffee is too hot to drink when served at 90°C. What is the mass of an ice cube, taken from a -20°C freezer, that will cool your coffee to a pleasant 60°C?