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

DS = 13865.7[J/K]

Step-by-step 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=(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]