Chapter 16, Problem 80GP

Thermal Storage Solar heating of a house is much more efficient if there is a way to store the thermal energy collected during the day to warm the house at night. Suppose one solar-heated home utilizes a concrete slab of area 12 m² and 25 cm thick. (a) If the density of concrete is 2400kg/m³, what is the mass of the slab? (b) The slab is exposed to sunlight and absorbs energy at a rate of 1.4 × 10⁷ J/h for 10 h. If it begins the day at 22 °C and has a specific heat of 750J/(kg.K), what is its temperature at sunset? (c) Model the concrete slab as being surrounded on both sides (contact area 24 m²) with a 2.0-m-thick layer of air in contact with a surface that is 5.0 °C cooler than the concrete. At sunset, what is the rate at which the concrete loses thermal energy by conduction through the air layer? (d) Model the concrete slab as having a surface area of 24 m² and surrounded by an environment 5.0 °C cooler than the concrete. If its emissivity is 0.94, what is the rate at which the concrete loses thermal energy by radiation at sunset?