The walls and roof in the home depicted have an average thickness of 22.0 cm and

Question

The walls and roof in the home depicted have an average thickness of

22.0 cm and an average thermal conductivity of 0.475 W/m

The walls and roof in the home depicted have an average thickness of 22.0 cm and an average thermal conductivity of 0.475 W/m middot ºC. Gas combustion is used to heat the home and the heater provides 9250 kcal per meter cubed of natural gas. How many 1 liter bottles of gas must be used each day to maintain in inside temperature of 26.0ºC if the outside temperature is 0.0ºC? Ignore radiation effects and energy transfer through the ground.

Explanation / Answer

Let x be the number of bottles for 1 day

Heat generated = {x/(24*60*60) }* {9250*1000* 4.18* 0.001} = x*0.4475 W

heat lost by conduction = K*A* (T2-T1)/L

we have L = 0.22 m , K = 0.475 W/mC , (T2-T1) = 26 -0 = 26 C

we find total area of house ,

the height of the triangle is given by (8/2) * Tan 37 = 3.0142 m

Hypotense of triangle = (8/2) sec(37) = 5.0085 m

A =2* ( 10*5) + 2*( 5*8) + 2*(0.5*8*3.0142) + 2*(10*5.0085) = 304.2836 m^2

so, heat lost by conduction = K*A* (T2-T1)/L = 0.475 * 304.2836* 26/0.22 = 17081.3748 W

so heat lost by conduction = heat generated

17081.3748 = x*0.4475

so x = 38170.669 = 38171 bottles

How many 1 liter bottles of gas must be used each day = 38171 bottles

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