Question

A boulder of mass 2000. kg breaks loose of a mountainside and plunges 200. m straight down into a lake at a temperature of 5.00◦C. Assuming the energy of the rock transforms into thermal energy, calculate the change in entropy of the lake.

Answer 1

Answer:

DS = 13865.7[J/K]

Explanation:

We can calculate the energy of the rock, like the potential energy relative to the lake level. Which can be calculated by means of the following expression of the potential energy:

$E_{p}=m*g*h\\\\where:\\m = mass = 2000[kg]\\h = elevation = 200 [m]\\g = gravity = 9.81[m/s^2]$

Therefore:

$E_{p}=2000*9.81*200\\E_{p}=3924000 [J]$

This energy is transformed into thermal energy.

we shall remember that isothermal heat transfer processes are internally reversible, so the entropy change of a system during one of these processes can be determined, by the following expression.

$DS=\frac{Q}{T}\\ where:\\DS = entropy change [J/K]\\Q = Heat transfer [J]\\T = temperature [K]$

T = 5 + 278 = 283[K]

DS = 3924000 / 283

DS = 13865.7[J/K]