Chapter 8
Direct Use of Solar Energy
Problem 8.1 Calculate the power radiated by a woodstove of dimensions 65 cm high by 55 cm
deep by 85 cm wide with a surface temperature of 120°C.
Assume that heat is radiated from all surfaces of the stove and that the stove has an emissivity of 1.
Note that woodstoves are painted black because black surfaces have high absorptance, and objects
with high absorptance also have high emissivity.
2
The surface area in m is (from sides/front/back/top/bottom)
The surface radiation is given by the Stefan-Boltzmann law as
P = AεσT
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Problem 8.3 Consider a vertical south-facing window in a house at 40ºN latitude. For an interior
temperature of 68ºF, make a plot of the minimum R-value as a function of outside temperature
from −20ºF to 50ºF for which the passive solar heating exceeds the heat loss though the window.
The heat loss through the window due to conduction per unit area per hour is (equation (8.5))
Problem 8.4 Compare the total solar energy received at the surface of the earth in one year to the
total annual global energy requirements.
Problem 8.5 Compare the RSI-values of:
a. Two pieces of 3-mm thick glass in thermal contact.
b. Two pieces of 3-mm thick glass with a 1-cm air space between them.
Problem 8.6 Approximate a house as a cube with an edge length of 20 ft.
The house loses heat from the four walls and the roof (but not the floor).
The average R-value for the walls and roof is R = 6.5 (this takes into account walls, windows,
doors, etc.).
3
Calculate the heat loss in Btu/ft per degree day (°F), and compare this to the estimated residential
heating needs discussed in this chapter.
Problem 8.7 A 75-gal (U.S.) electric hot water heater has provides 9000 W of power to heat water.
If the heater is filled with water at an initial temperature of 50°F, how long will it take for the
water to reach 140°F? Assume there are no heat losses.
The heat is
Q = CmΔT
Problem 8.8 Compare the masses and volumes of water, concrete, sand, and wood needed to store
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10 Btu of heat if the operating temperatures are Tc = 85ºF and Th = 180ºF. In each case, calculate
the edge length of a square storage unit with a height of 8 ft.
The amount of heat (thermal energy) stored is given by equation (8.12) as
Q = mCΔT
Solving for mass gives
m = Q/(CΔT)