Question

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 14 m2 and 21 cm thick.

A) If the density of concrete is 2400 kg/m3, what is the mass of the slab?

Express your answer to two significant figures and include appropriate units.

b)

The slab is exposed to sunlight and absorbs energy at a rate of 1.7 ×107J/h for 10 h. If it begins the day at 25 ∘C and has a specific heat of 750 J/(kg⋅K), what is its temperature at sunset?

c) Model the concrete slab as being surrounded on both sides (contact area 28 m2) with a 1.7-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 0.93, what is the rate at which the concrete loses thermal energy by radiation at sunset?

Answer 1

( A )

If the density of concrete is 2400 kg/m3,

mass of the slab = 2400*14*21*0.01 = 7056 kg/m3

( B )

The slab is exposed to sunlight and absorbs energy at a rate of 1.7 ×107J/h for 10 h. If it begins the day at 25 ∘C and has a specific heat of 750 J/(kg⋅K).

We know that ∆Q = ρ.c_p.∆T

Say temperature at sunset  

( C )

Rate of dissipation of thermal energy at the time of sunset is

Temperature difference is 5 K

∆Q = ρ.c_p.∆T= 2400 * 750 * 5 = 9000000 J / h per unit area

( D )

The rate at which the concrete loses thermal energy by radiation at sunset

=0.29182 J / h