The concrete slab of a basement is 11 m long, 8 m wide, and 0.20 m thick. during the winter, temperatures are nominally 17°c and 10°c at the top and bottom surfaces, respectively. if the concrete has a thermal conductivity of 1.4 w/m·k, what is the rate of heat loss through the slab? if the basement is heated by a gas furnace operating at an efficiency of ηf = 0.90 and natural gas is priced at cg = $0.02/mj, what is the daily cost of the heat loss?

so heat loss =  4312 W

cost of heat loss daily is $8.28 per day

Explanation:

given data

slab length L = 11 m

slab wide W = 8 m

thickness t = 0.20 m

temperature top T1 = 17°C

temperature bottom T2 = 10°C

thermal conductivity k = 1.4 W/m-K

efficiency ηf = 0.90

priced  Cg = $0.02 / MJ

to find out

rate of heat loss and daily cost of the heat loss

solution

we calculate here heat loss by heat transfer

so apply here formula that is

q = (thermal conductivity × area × temperature difference) / thickness

put here all these value we get heat loss

q  =

q  =

q = 4312 W

so heat loss =  4312 W

and

cost of the heat loss is express as

cost of heat loss =

put here all these value

cost of heat loss is =  × 24 hr/day × 3600 s/hr

cost of heat loss = 8.279

so cost of heat loss daily is $8.28 per day

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