A raindrop (mass 1.00 g) is travelling at a speed of 40m/s when it hits the surface of 100 g of water contained in a drinking glass. What is the change in temperature of the water in the glass if we assume that a) all the kinetic energy of the raindrop is converted to energy that changes the water's temperature, and b) the water in the glass and the raindrop was at the same original temperature?

Question

A raindrop (mass 1.00 g) is travelling at a speed of  40m/s when it hits the surface of 100 g of water contained in a drinking glass. What is the change in temperature of the water in the glass if we assume that a) all the kinetic energy of the raindrop is converted to energy that changes the water's temperature, and b) the water in the glass and the raindrop was at the same original temperature?

drwls · Answer

1.00 g is a lot more than a raindrop of water. Its kinetic energy is
(1/2)MV^2 = (1/2)*(1.0)*(1600) = 800J
= 191 calories

That amount of KE gets converted to heat (Q) and added to the internal energy of 101 g of water.

The temperature change is
deltaT = Q/(M*C)
where C is the specific heat of liquid water, 1.0 Cal/g*C

deltaT = 191/101 = 1.89 C