20. Heat and Temperature

A rigid container holds $12\mathrm{g}$ of ${\mathrm{O}}_2$ gas at $30°\mathrm{C}$. How much energy must be added to the gas to bring its temperature to $50°\mathrm{C}$?

The blood plays an important role in removing heat from the body by bringing this energy directly to the surface where it can radiate away. Nevertheless, this heat must still travel through the skin before it can radiate away. Assume that the blood is brought to the bottom layer of skin at 37.0°C and that the outer surface of the skin is at 30.0°C. Skin varies in thickness from 0.50 mm to a few millimeters on the palms and soles, so assume an average thickness of 0.75 mm. A 165-lb, 6-ft-tall person has a surface area of about 2.0 m2 and loses heat at a net rate of 75 W while resting. On the basis of our assumptions, what is the thermal conductivity of this person's skin?

Two rods, one made of brass and the other made of copper, are joined end to end. The length of the brass section is 0.300 m and the length of the copper section is 0.800 m. Each segment has cross-sectional area 0.00500 m^2 . The free end of the brass segment is in boiling water and the free end of the copper segment is in an ice–water mixture, in both cases under normal atmospheric pressure. The sides of the rods are insulated so there is no heat loss to the surroundings. (b) What mass of ice is melted in 5.00 min by the heat conducted by the composite rod?

The emissivity of tungsten is 0.350. A tungsten sphere with radius 1.50 cm is suspended within a large evacuated enclosure whose walls are at 290.0 K. What power input is required to maintain the sphere at 3000.0 K if heat conduction along the supports is ignored?

A spherical pot contains 0.75 L of hot coffee (essentially water) at an initial temperature of 95°C. The pot has an emissivity of 0.60, and the surroundings are at 20.0°C. Calculate the coffee's rate of heat loss by radiation.

An electric kitchen range has a total wall area of 1.40 m^2 and is insulated with a layer of fiberglass 4.00 cm thick. The inside surface of the fiberglass has a temperature of 175°C, and its outside surface is at 35.0°C. The fiberglass has a thermal conductivity of 0.040 W/m K. (a) What is the heat current through the insulation, assuming it may be treated as a flat slab with an area of 1.40 m^2 ?

Suppose that the rod in Fig. 17.24a is made of copper, is 45.0 cm long, and has a cross-sectional area of 1.25 cm^2 . Let TH = 100.0°C and TC = 0.0°C. (a) What is the final steady-state temperature gradient along the rod?

Most stars are main-sequence stars, a group of stars for which size, mass, surface temperature, and radiated power are closely related. The sun, for instance, is a yellow main-sequence star with a surface temperature of 5800 K. For a main-sequence star whose mass M is more than twice that of the sun, the total radiated power, relative to the sun, is approximately P/Pₛᵤₙ=1.5(M/Mₛᵤₙ)^3.5 . The star Regulus A is a bluish main-sequence star with mass 3.8Mₛᵤₙ and radius 3.1Rₛᵤₙ. What is the surface temperature of Regulus A?

Liquid helium, with a boiling point of 4.2 K, is used in ultralow-temperature experiments and also for cooling the superconducting magnets used in MRI imaging in medicine. Storing liquid helium so far below room temperature is a challenge because even a small 'heat leak' will boil the helium away. A standard helium dewar, shown in FIGURE P19.67, has an inner stainless-steel cylinder filled with liquid helium surrounded by an outer cylindrical shell filled with liquid nitrogen at –196°C. The space between is a vacuum. The small structural supports have very low thermal conductivity, so you can assume that radiation is the only heat transfer between the helium and its surroundings. Suppose the helium cylinder is 16 cm in diameter and 30 cm tall and that all walls have an emissivity of 0.25. The density of liquid helium is 125 kg/m^3 and its heat of vaporization is 2.1×10^4 J/kg.a. What is the mass of helium in the filled cylinder?

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 24×10^5 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.)

A 5.0-m-diameter garden pond is 30 cm deep. Solar energy is incident on the pond at an average rate of 400 W/m^2. If the water absorbs all the solar energy and does not exchange energy with its surroundings, how many hours will it take to warm from 15°C to 25°C?

You are boiling pasta and absentmindedly grab a copper stirring spoon rather than your wooden spoon. The copper spoon has a 20 mm ×1.5 mm rectangular cross section, and the distance from the boiling water to your 35°C hand is 18 cm. How long does it take the spoon to transfer 25 J of energy to your hand?

The ends of a 20-cm-long, 2.0-cm-diameter rod are maintained at 0°C and 100°C by immersion in an ice-water bath and boiling water. Heat is conducted through the rod at 4.5×10^4 J per hour. Of what material is the rod made?

A 100 cm³ box contains helium at a pressure of 2.0 atm and a temperature of 100℃. It is placed in thermal contact with a 200 cm³ box containing argon at a pressure of 4.0 atm and a temperature of 400℃.c. How much heat energy is transferred, and in which direction?