A pond with a flat bottom has a surface area of 820 m^2 and a depth of 2.0m. on a warm day, the surface water is a temperature of 25 deg C, while the bottom of the pond is at 12 deg C. Find the rate at which energy is transferred by conduction from the surface to the bottom of the pond.
To find the rate at which energy is transferred by conduction from the surface to the bottom of the pond, we can use the formula:
Q = k * A * (T1 - T2) / d
Where:
Q = Rate of energy transfer by conduction
k = Thermal conductivity of water
A = Surface area of the pond bottom
T1 = Surface temperature of the water
T2 = Bottom temperature of the water
d = Thickness or depth of the pond
From the given information:
A = 820 m^2
T1 = 25 °C
T2 = 12 °C
d = 2.0 m
However, we still need the value for the thermal conductivity of water (k). The thermal conductivity of water depends on various factors such as temperature and impurities. For simplicity, we can use the approximate value of 0.6 W/(m·K) for the thermal conductivity of water.
Plugging in the values into the formula:
Q = 0.6 * 820 * (25 - 12) / 2.0
Simplifying the expression:
Q = 0.6 * 820 * 13 / 2.0
Q ≈ 3036 W
Therefore, the rate at which energy is transferred by conduction from the surface to the bottom of the pond is approximately 3036 watts.
To find the rate at which energy is transferred by conduction from the surface to the bottom of the pond, we need to calculate the heat transfer using the formula:
Q = k * A * (dT / d)
Where:
Q is the rate of heat transfer (in joules per second or watts)
k is the thermal conductivity of water (which is approximately 0.6 W/m·K)
A is the surface area of the pond (820 m^2)
dT is the temperature difference between the surface and the bottom (25 - 12 = 13 deg C)
d is the thickness or depth of the pond (2.0 m)
Plugging in the values, we have:
Q = 0.6 * 820 * (13 / 2.0)
Calculating this expression gives us the rate of heat transfer, Q, from the surface to the bottom of the pond in joules per second or watts.