From a height of 35.0 m, a 1.25 kg bird dives (from rest) into a small fish tank containing 50.0 kg of water.
What is the maximum rise in temperature of the water if the bird gives it all of its mechanical energy?
(delta)T= ?? degrees C
First compute the mechanical energy that is converted to heat, Q.
Q = (1/2) M g H
H = 35 m
g = 9.8 m/s^2
M = 1.25 kg. Q will be in Joules if you use these units. Divide the number of Joules by 4.18 to get calories
To get the delta T, use
Q = M(water) * C * (delta T)
C = 1.00*10^3 calories/kg C
I'm not getting the correct answer.. this is my work:
Q=214.374/4.18 =51.286
51.286=(50)(10^3)T
T=.001
Do I need to convert the T to something else? It says to have it in C, which I think it's already in...
To find the maximum rise in temperature of the water, we need to calculate the mechanical energy transferred from the bird to the water.
First, let's calculate the potential energy of the bird when it is at a height of 35.0 m. The potential energy can be calculated using the equation:
Potential energy = mass * gravitational acceleration * height
Since the mass of the bird is 1.25 kg, the gravitational acceleration is 9.8 m/s^2, and the height is 35.0 m, we have:
Potential energy = 1.25 kg * 9.8 m/s^2 * 35.0 m
Next, we need to find the amount of mechanical energy that is transferred to the water. Since the bird gives all of its mechanical energy to the water, this energy will be equal to the potential energy calculated above.
Now, we can calculate the rise in temperature of the water using the specific heat capacity formula:
Energy = mass * specific heat capacity * change in temperature
In this case, the mass of the water is 50.0 kg, and we want to find the change in temperature. Rearranging the equation, we have:
Change in temperature = Energy / (mass * specific heat capacity)
Since we have already found the energy transferred (potential energy of the bird), we can substitute the values into the equation:
Change in temperature = (Potential energy of the bird) / (mass of water * specific heat capacity)
By plugging in the numbers and values, you can calculate the change in temperature, which will give you the maximum rise in temperature of the water.