Question

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 10 ∘C at the top and bottom surfaces, respectively. If the concrete has a thermal conductivity of 1.4W/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 nf =0.90 and natural gas is priced at C g$0.02/MJbwhat is the daily cost of the heat loss?

Answer 1

To calculate the rate of heat loss through the concrete slab, use the formula: Q = k * A * (T2 - T1) / d. To calculate the daily cost of the heat loss, multiply the rate of heat loss by the cost of natural gas and the efficiency of the gas furnace.

Step-by-step explanation:

To calculate the rate of heat loss through the concrete slab, we can use the formula: Q = k * A * (T2 - T1) / d, where Q is the rate of heat loss, k is the thermal conductivity of the concrete, A is the area of the slab, T2 is the temperature at the top surface, T1 is the temperature at the bottom surface, and d is the thickness of the slab.

Plugging in the values: Q = 1.4W/m K * (11m * 8m) * (17°C - 10°C) / 0.20m. Solving this equation will give us the rate of heat loss through the slab.

To calculate the daily cost of the heat loss, we can multiply the rate of heat loss by the cost of natural gas and the efficiency of the gas furnace. The formula is: Cost = Q * nf * Cg, where Cost is the daily cost, Q is the rate of heat loss, nf is the efficiency of the gas furnace, and Cg is the cost of natural gas.

Plugging in the values: Cost = Q * 0.90 * 0.02. Solving this equation will give us the daily cost of the heat loss.