Question

While painting the top of an antenna 227 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break.

a)If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes into the water, what is its increase in temperature?

answer is in C

Answer 1

Here, volume of water = 1L = 0.001 m^3

density of water 1000 kg/m^3

so, Mass of water in bottle = volume * density = 1000 * 0.001 = 1 kg

Height from where, water bottle falls, h = 227 m

On falling from height h to fround level, Change in mechanical energy = Change in potential energy

PE at height h = mgh = 1 * 9.8 * 227 = 2224.6 J

PE at ground level = 0

Change in mechanical energy = 2224.6 J

Now heat generated = change in mechanical energy

and heat generated , Q = mcT

here, m is mass of water = 1 kg

c is specific heat of water = 4186 J/kg C

so, change in temperature , T = Q/mc = 2224.6/4186 = 0.531 C