From a height of 30.5 , a 1.45 bird dives (from rest) into a small fish tank containing 49.0 of water. What is the maximum rise in temperature of the water if the bird gives it all of its mechanical energy?
To calculate the maximum rise in temperature of the water, we need to consider the conservation of energy. The potential energy of the bird at the initial height is converted into kinetic energy as it dives, and then into thermal energy when it hits the water.
First, let's calculate the potential energy of the bird at a height of 30.5m. The potential energy formula is:
Potential Energy = mass * gravity * height
Given that the mass of the bird is 1.45kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the potential energy:
Potential Energy = 1.45 kg * 9.8 m/s² * 30.5 m
Next, we need to consider the conversion of potential energy into kinetic energy. When the bird is about to hit the water, all of its potential energy is converted into kinetic energy. The kinetic energy formula is:
Kinetic Energy = (1/2) * mass * velocity^2
Since the bird starts from rest, its initial velocity is 0 m/s. So its final velocity is given by the equation:
Final Velocity = √(2 * Potential Energy / mass)
Now, using the final velocity, we can calculate the kinetic energy of the bird:
Kinetic Energy = (1/2) * mass * (Final Velocity)^2
The total energy transferred to the water is equal to the kinetic energy of the bird, which gets converted into thermal energy when it hits the water. This energy transfer can be calculated using the equation:
Energy transferred = mass of water * specific heat capacity of water * change in temperature
Given that the mass of water is 49.0 kg and the specific heat capacity of water is approximately 4.18 J/g°C, we can now calculate the change in temperature:
Change in temperature = Energy transferred / (mass of water * specific heat capacity of water)
Finally, we can substitute the value of energy transferred into the equation to calculate the change in temperature, which represents the maximum rise in temperature of the water.