Numerical Problem 1: Water at 200 C falls from a height of 854 meters. If the whole energy used in increasing the temperature, find out the final temperature. Specific heat of water is 4200 Jk-1 Kg-1.
Theory: When water is at a height 854 m, it possesses some potential energy. When it falls down, this energy is converted to kinetic energy. The kinetic energy converts to heat to increase the temperature of water. So in fact, the heat energy will be equal to the P.E at the top.
Similarly, if ΔQ is the heat, m is the mass and ΔT is raise in temperature of a substance, then
Compare the two equations,
So, final temperature will be = initial temperature at top + change in temperature at bottom
Final temperature = 20° + 1.99°C = 21.99°C ≅ 22°C