How does the work done by a falling weight affect the temperature of water?
What is the relationship between the work done by a falling weight and the temperature increase in water?
Given data:
- Mass of the weight (m) = 272.8 kg
- Final velocity of the weight (vf) = 3.000 m/s
- Specific heat of water (c) = 4182 J/(kg K)
- Mass of the water (M) = 1.988 kg
How does the energy transferred from the work done by the falling weight result in a temperature increase in the water?
Explanation:
The work done by the falling weight raises the temperature of 1.988 kg of water by approximately 1.0231 Kelvin. To calculate the temperature increase in the water caused by the work done by the falling weight, we need to use the principle of energy conservation.
When a 272.8-kg weight attached to a paddle wheel in oil falls from rest to 3.000 m/s, the work done by the falling weight is eventually transferred to the water with nearly no loss to other forms of energy. This work done by the falling weight is equal to the change in kinetic energy of the weight as it falls. The energy transferred to the water from this work done results in a temperature increase in the water.
To calculate the temperature increase, we use the formula: Temperature increase = Work / (M * c). Substituting the given values and the calculated work value, we can determine that the temperature of 1.988 kg of water increases by approximately 1.0231 Kelvin from the energy transferred from the falling weight.
This relationship demonstrates how the work done by a falling weight can lead to a temperature change in water, highlighting the interconnected nature of energy transfer and thermal effects. Understanding this concept is crucial in various fields of physics and engineering where energy conversion and thermal management play key roles.