A 5kg voulume of water falls from a shelf 2 meters above the floor, If all the energy is converted to heat, what is the change in temperature?
To calculate the change in temperature of the water, we can use the principle of conservation of energy. The potential energy of the water when it falls is converted into heat energy.
First, let's calculate the potential energy (PE) of the water using the formula PE = m * g * h, where m is the mass of the water, g is the acceleration due to gravity, and h is the height from which it falls.
Given:
Mass of water (m) = 5 kg
Height (h) = 2 m
Acceleration due to gravity (g) ≈ 9.8 m/s²
PE = m * g * h
PE = 5 kg * 9.8 m/s² * 2 m
PE = 98 J
The potential energy is 98 Joules.
Now, we need to find the change in temperature (ΔT) of the water using the specific heat capacity equation Q = m * c * ΔT, where Q is the heat energy, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
The specific heat capacity of water is approximately 4186 J/kg°C.
Substituting the known values:
Q = 98 J
m = 5 kg
c = 4186 J/kg°C
Q = m * c * ΔT
98 J = 5 kg * 4186 J/kg°C * ΔT
Solving for ΔT:
ΔT = 98 J / (5 kg * 4186 J/kg°C)
ΔT ≈ 0.00467 °C
Therefore, the change in temperature of the water when all the energy is converted to heat is approximately 0.00467 °C.