20. Heat and Temperature

A ceramic cube 3.0 cm on each side radiates heat at 630 W. At what wavelength, in μm, does its emission spectrum peak? Assume e=1.

A house has a volume of 1200 m³. What is the total mass of air inside the house at 15°C?

(I) To what temperature will 6800 J of heat raise 3.0 kg of water that is initially at 10.0°C?

(II) A small immersion heater is rated at 375 W. Estimate how long it will take to heat a cup of soup (assume this is 250 mL of water) from 15°C to 75°C.

(I) One end of a 64-cm-long copper rod with a diameter of 2.0 cm is kept at 460°C, and the other is immersed in water at 22°C. Calculate the heat conduction rate along the rod.

A leaf of area 40cm² and mass 4.5 x 10⁻⁴ kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kgK. Estimate the energy absorbed per second by the leaf from the Sun.

(II) Heat conduction to skin. Suppose 150 W of heat flows by conduction from the blood capillaries beneath the skin to the body’s surface area of 1.5 m². If the temperature difference is 0.50 C°, estimate the average distance of capillaries below the skin surface.

(II) When a diver jumps into the ocean, water leaks into the gap region between the diver’s skin and her wetsuit, forming a water layer about 0.5 mm thick. Assuming the total surface area of the wetsuit covering the diver is about 1.0m², and that ocean water enters the suit at 10°C and is warmed by the diver to skin temperature of 35°C, estimate how much energy (in units of candy bars = 300kcal) is required by this heating process.

(a) How much power is radiated by a tungsten sphere (emissivity ∈ = 0.35) of radius 19 cm at a temperature of 25°C?

(b) If the sphere is enclosed in a room whose walls are kept at - 5 °C, what is the net flow rate of energy out of the sphere?

A copper rod and an aluminum rod of the same length and cross-sectional area are attached end to end (Fig. 19–35). The copper end is placed in a furnace maintained at a constant temperature of 205°C. The aluminum end is placed in an ice bath held at a constant temperature of 0.0°C. Calculate the temperature at the point where the two rods are joined.

(a) Estimate the total power radiated into space by the Sun, assuming it to be a perfect emitter at T = 5500 K. The Sun’s radius is 7.0 x 10⁸ m.

(b) From this, determine the power per unit area arriving at the Earth, 1.5 x 10¹¹ m away (Fig. 19–37).

A 12-g lead bullet traveling at 220 m/s passes through a thin wall and emerges at a speed of 160 m/s. If the bullet absorbs 50% of the heat generated, If the bullet’s initial temperature was 20°C, will any of the bullet melt, and if so, how much?

In a cold environment, a person can lose heat by conduction and radiation at a rate of about 200 W. Estimate how long it would take for the body temperature to drop from 36.6°C to 35.6°C if metabolism were nearly to stop. Assume a mass of 65 kg. (See Table 19–1.)

A leaf of area 40cm² and mass 4.5 x 10^-4 kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kg K. Estimate the rate of rise of the leaf’s temperature.

A mountain climber wears a goose-down jacket 3.8 cm thick with total surface area 0.95 m². The temperature at the surface of the clothing is -18°C and at the skin is 34°C. Determine the rate of heat flow by conduction through the jacket assuming (a) it is dry and the thermal conductivity k is that of goose down, and (b) the jacket is wet, so k is that of water and the jacket has matted to 0.50 cm thickness.