Question

What is the difference in temperature of water at the top and bottom of a rainfall of height 500 mts. (Specific heat of water = 10^3 cal/kg & J = 4.2 J/cal).

Answer 1

Answer:

Temperature difference is 1.17 K.

Step by step explanation:

The energy gained by water falling: $E=mgh$, where m is the mass of water, g is the gravitational force (9.8 $m/sec^2$) and h is the height.

Energy causing rise in temperature is: $E=m*c*dT$; where c is the specific heat capacity of water (in J/kg.K) and dT is the change in temperature.

The two energies must be equal.

Therefore, $m*h*g=m*c*dT\\dT=\frac{hg}{c}$.

First we need to convert the specific heat capacity of water from 1000 cal/kg to J/kg.K; which is 4186 J/kg*K.

Therefore, $dT=\frac{500*9.8}{4186}\\ =1.17\:K$