What is the temperature change?

Question

A rain drop of mass 1.00 g is falling from the roof of 82.0m tall building and hits the surface of 100.0g of water contained in a glass standing on the ground.Ignore air resistance of the drop. Assume that the water in the glass is perfectly insulated,all the mechanical energy of the raindrop is converted to energy that changes the water's temperature, and the water in the glass and the raindrop were at the same original temperature. What is the change in temperature of the water in the glass?

Answer 1

A rain drop of mass 1.00 g is falling from the roof of 82.0m tall building and hits the surface of 100.0g of water contained in a glass standing on the ground.Ignore air resistance of the drop. Assume that the water in the glass is perfectly insulated,all the mechanical energy of the raindrop is converted to energy that changes the water's temperature, and the water in the glass and the raindrop were at the same original temperature. What is the change in temperature of the water in the glass

Convert all units to SI.

The potential energy of the water drop is .001kg x 82m x 9.81 = 0.804J

When this drop of water merges into the glass, the increase in energy dictates the increase in temperature

ΔQ = mcΔT

0.804J/(0.101kg x 4200) = ΔT = 1.9 x 10^-3 K

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