A slab of a thermal insulator is 100 cm² in cross section and 2 cm thick. Its thermal conductivity is 2.4 x 10-4 cal/s.cm.°C. If the temperature difference between the opposite faces is 100 degrees Celsius, how much heat flows through the slab in one day?
To calculate the amount of heat that flows through the slab in one day, we need to use the formula for heat conduction:
Q = k * A * ΔT / Δx
Where:
Q = Amount of heat transferred
k = Thermal conductivity
A = Cross-sectional area
ΔT = Temperature difference
Δx = Thickness of the slab
Let's break down the given information:
Cross-sectional area (A) = 100 cm²
Thickness (Δx) = 2 cm
Thermal conductivity (k) = 2.4 x 10^-4 cal/s.cm.°C
Temperature difference (ΔT) = 100 °C
Now, let's substitute these values into the formula:
Q = (2.4 x 10^-4 cal/s.cm.°C) * (100 cm²) * (100 °C) / (2 cm)
First, we'll simplify the equation:
Q = (2.4 x 10^-4) * (100) * (100) / (2)
Q = 0.024 * 100 * 100 / 2
Q = 2400 / 2
Q = 1200 cal
So, 1200 calories of heat will flow through the slab in one day.
To calculate the heat flow through the slab in one day, we can use the formula:
Heat flow (Q) = (thermal conductivity x cross-sectional area x temperature difference) / thickness
Given:
- Cross-sectional area (A) = 100 cm²
- Thickness (L) = 2 cm
- Thermal conductivity (k) = 2.4 x 10^(-4) cal/s.cm.°C
- Temperature difference (ΔT) = 100 degrees Celsius
Substituting the values into the formula:
Q = (2.4 x 10^(-4) cal/s.cm.°C x 100 cm² x 100 °C) / 2 cm
First, let's convert the units to a more convenient format:
1 cal/s = 86,400 cal/day (since there are 86,400 seconds in a day)
1 cm² = 0.0001 m² (since 1 m² = 10,000 cm²)
Q = (2.4 x 10^(-4) cal/s.cm.°C x 100 cm² x 100 °C x 86,400 cal/day) / (2 cm)
Q = (2.4 x 10^(-4) x 100 x 100 x 86,400) / 2 cal/day
Calculating the expression:
Q = (0.0024 x 1,000,000 x 86,400) / 2 cal/day
Q = 124,416,000 cal/day
Therefore, approximately 124,416,000 calories flow through the slab in one day.
heat flow=conductivity*area/distance*(temp difference)*timeinSeconds
= 2.4e-4(100/2)(100)*(3600*24) calories