A waterfall is 420m high, calculate the difference in temperature of the water between the top and the bottom of the waterfall = 4.20 × 10^3 jkg [k^-1= 10^-2]?
To calculate the difference in temperature of the water between the top and bottom of the waterfall, we need to use the formula:
ΔT = (ΔE) / (m * Cp)
Where:
ΔT = difference in temperature
ΔE = change in energy
m = mass of the water
Cp = specific heat capacity of water
Given:
Height of the waterfall (h) = 420m
Change in potential energy (ΔE) = 4.20 × 10^3 Jkg
Specific heat capacity of water (Cp) = 10^2 Jkg^-1K^-1
First, let's calculate the mass of the water:
mass (m) = ΔE / g / h
where g is the acceleration due to gravity (approximately 9.8 m/s^2)
mass (m) = (4.20 × 10^3 Jkg) / (9.8 m/s^2) / (420 m)
mass (m) ≈ 1.01 kg
Now, we can calculate the difference in temperature:
ΔT = (4.20 × 10^3 Jkg) / (1.01 kg) / (10^2 Jkg^-1K^-1)
ΔT ≈ 41.58 K
Therefore, the difference in temperature of the water between the top and bottom of the waterfall is approximately 41.58 degrees Celsius.
To calculate the difference in temperature of the water between the top and bottom of a waterfall, we can use the equation:
ΔT = (ΔQ / mc)
Where:
ΔT is the difference in temperature,
ΔQ is the heat energy transferred,
m is the mass of water,
c is the specific heat capacity of water.
In this case, we are given the heat energy transferred per kilogram of water (jkg^-1k^-1) and the height of the waterfall.
To find ΔQ, we can use the formula:
ΔQ = mgh
Where:
m is the mass of water (in kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
h is the height of the waterfall (in meters).
Given that the waterfall is 420m high, we can substitute these values into the equation:
ΔQ = m * 9.8 * 420
Now, substituting the given value for ΔQ (4.20 × 10^3 jkg^-1k^-1), we can solve for m:
4.20 × 10^3 = m * 9.8 * 420
Simplifying the equation:
m = (4.20 × 10^3) / (9.8 * 420)
m ≈ 0.00106 kg
Now that we know the mass of water (m), we can calculate the difference in temperature (ΔT) by substituting the values into the first equation:
ΔT = (ΔQ / mc)
ΔT = (4.20 × 10^3) / (0.00106 * c)
Given that the specific heat capacity of water is 4.20 × 10^3 jkg^-1k^-1, we can substitute this value into the equation:
ΔT = (4.20 × 10^3) / (0.00106 * 4.20 × 10^3)
Simplifying the equation:
ΔT = 1 / 0.00106
ΔT ≈ 943.39 Kelvin
Therefore, the difference in temperature of the water between the top and bottom of the waterfall is approximately 943.39 Kelvin.