The amount of energy needed to increase the temperature of a substance by
is given by:
where
m is the mass of the substance
is the specific heat capacity of the substance
is the increase of temperature
In our problem,
, while
and the specific heat capacity of iron is
if we plug these numbers in the equation, we find the amount of energy needed:
The complete question is;
James Joule (after whom the unit of energy is named) claimed that the water at the bottom of Niagara Falls should be warmer than the water at the top, 51 m above the bottom. He reasoned that the falling water would transform its gravitational potential energy at the top into thermal energy at the bottom, where turbulence brings the water almost to a halt. If this transformation is the only process occurring, how much warmer will the water at the bottom be?
Answer:
Water becomes warmer by a temperature of ΔT = 0.119 K
Explanation:
If we assume that gravitational kinetic energy will be converyrf into thermal enrgy, we will have;
Q = U
So, m•c_w•ΔT = mgh
Where;
c_w is specific heat capacity of water with a value of 4184 J/Kg.K
ΔT is change in temperature indicating how warmer the water will be. Thus making ΔT the subject, we have;
ΔT = gh/c_w
So, ΔT = 9.8 x 51/4184 = 0.119 K
Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2<span>) electrons.</span>