James Prescott Joule, after whom the unit of energy is named, wanted to prove that mechanical energy can be converted to thermal energy. To help him prove that,he created the setup as shown in the figure.
1kg of water is stored in an adiabatic container at 15∘C. A paddle connected to a mass of 15 kgs through massless and frictionless pulleys, is immersed into the water.
At time t = 0s, the 15kg mass is allowed to fall. After 40s it was noticed that the mass had fallen by a height of 10 m and gained a velocity of 4 m/s. If Joule was successful in this experiment, what would be the temperature of the water at time t = 40s?
The mass of 15kgs starts from rest from position A. As it moves down it loses potential energy and gains kinetic energy.
The mass also drives the paddle immersed in water.
Since total energy will be conserved, the potential energy lost by the mass must be equal to the sum of kinetic energy gained by it and the work done to drive the paddle.
P.E lost = K.E. gained + work done on the paddle W.
⇒ work or paddle W = 1350 J.
The work done on the paddle is absorbed by the water, which resists the paddle motion.So the temperature gained by water can be calculated by the formula -
Q = work done on paddle= mc ΔT,
m = mass of water = 1 kg
c = specific heat = 4200 J/kg K.
ΔT=0.32∘C or 0.32K.