20. Heat and Temperature

(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.

Estimate the rate at which heat can be conducted from the interior of the body to the surface. As a model, assume that the thickness of tissue is 4.0 cm, that the skin is at 34°C and the interior at 37°C, and that the surface area is 1.5m². Compare this to the measured value of about 230 W that must be dissipated by a person working lightly. This clearly shows the necessity of convective cooling by the blood.

A leaf of area 40 cm² 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. Will the temperature rise continue for hours? Why or why not?

(a) Using the solar constant, estimate the rate at which the whole Earth receives energy from the Sun. (b) Assume the Earth radiates an equal amount back into space (that is, the Earth is in equilibrium). Then, assuming the Earth is a perfect emitter, (∈ = 1.0) estimate its average surface temperature. [Hint: Discuss why you use area A = πr²_E or A = 4πr²_E in each part.]