How much heat is lost in one hour through a 0.15 m × 3.7 m × 6.1 m concrete floor if the inside temperature is 22.0 °C and the ground temperature is 13.0 °C?
To calculate the amount of heat lost through a concrete floor, we can use the formula:
Q = U * A * (T1 - T2) * t
Where:
Q = amount of heat lost (in joules)
U = overall heat transfer coefficient (in W/m^2·K)
A = surface area of the floor (in m^2)
T1 = inside temperature (in Kelvin)
T2 = ground temperature (in Kelvin)
t = time period (in seconds)
First, we need to convert the temperatures from Celsius to Kelvin:
T1 = 22.0 + 273.15 = 295.15 K
T2 = 13.0 + 273.15 = 286.15 K
Next, we need to determine the overall heat transfer coefficient (U) for the concrete floor. The overall heat transfer coefficient takes into account the thermal conductivity of the material and any additional factors such as insulation. Without this information, we cannot accurately calculate U. However, for the purpose of this explanation, let's assume a hypothetical value of U = 2 W/m^2·K.
Now, we can calculate the amount of heat lost:
Q = 2 * (0.15 * 3.7) * (295.15 - 286.15) * (1 hour * 3600 seconds/hour)
Q ≈ 2 * 0.555 * 9 * 3600
Q ≈ 36,036 joules
So, approximately 36,036 joules of heat are lost in one hour through a concrete floor with the given dimensions and temperature difference.