Most houses are not airtight: air goes in and out around doors and windows, through cracks and crevices, following wiring to switches and outlets, and so on. The air in a typical house is completely replaced in less than an hour. Suppose that a moderately-sized house has inside dimensions 12.0m x 18.0m x 3.00m high, and that all air is replaced in 30.0 min. Calculate the heat transfer per unit time in watts needed to warm the incoming cold air by 10.0°C, thus replacing the heat transferred by convection alone.

Strategy

Heat is used to raise the temperature of air so that Q = mcΔT. The rate of heat transfer is then Q/t, where t is the time for air turnover. We are given that ΔT is 10.0°C, but we must still find values for the mass of air and its specific heat before we can calculate Q. The specific heat of air is a weighted average of the specific heats of nitrogen and oxygen, which gives c = C_p ≅ 1000 J/kg.°C from Table 14.1 (note that the specific heat at constant pressure must be used for this process).

Data given in Table 14.1

Transcribed Image Text:

Aluminum Asbestos Copper Concrete, granite (average) Glass Gold Substances Human body (average at 37 °C) Ice (average, -50°C to 0°C) Iron, steel Lead Silver Solids Wood J(kg°C) 900 800 840 387 840 129 3500 2090 452 128 235 Specific heat (c) 1700 kcal(kg°C) ¹ 0.215 0.19 0.20 0.0924 0.20 0.0308 0.83 0.50 0.108 0.0305 0.0562 0.4