Question

A) Suppose you dump a bucket of water (5.00kg at 15.0C) outside on a cold night where T = -10.0C, and the water spreads out over an area so large that the temperature of the ground remains at -10.0C, acting like an ideal “cold reservoir.” Calculate the entropy change of the water in going from 15.0C to -10.0C, and calculate the entropy change of the environment, absorbing heat while staying (approximately) at -10.0C. This problem requires you to use TWO equations for entropy change – of a substance changing temperature and for a substance with Q in or out but at constant T. I got somewhat less than 8000J/K for the “environment’s” ∆S.

B) Use your answers to part A to solve for the total entropy change of the UNIVERSE in that process (ie, add the entropy changes of all the parts, confirming that the entropy change of the UNIVERSE is positive.)

C) Some people uncomfortable with the idea of evolution try to argue against it because, they say, it says that more “ordered” organisms evolve from less ordered organisms. Since entropy is a measure of “disorder,” this can’t happen. Now suppose for a moment that if you really did calculate the entropy of a bunch of “biomass” of 1 billion years ago, full of primitive organisms and a few inorganic compounds, and the equivalent “biomass” of a few people, and you found that the entropy WAS lower for the people, indicating that, yes indeed, the more complex organisms DO have lower entropy than the equivalent “primitive stuff” of which they were made. Why does this STILL not violate the second law of thermodynamics? (Hint: is part B fundamentally different from part A of this exercise, or are they fundamentally the same?)

Answer 1

1) The entropy = Heat / Temperature

a) System : Water to ice

The heat released = Heat released in cooling water from 15 C to 0C + Heat released in conversion of water to ice + heat released in cooling ice from 0 C to 10C

q1 = Mass of water X change in temperature X specific heat

q1 = 5000 X (15°C) (4.184 J g¯¹ °C¯¹) = 12,878 J = 313.8 KJ

q2 = (6.02 kJ/mol) (5000g / 18.0 g/mol) = 1672.2 KJ

q3 = Mass of ice X change in temperature X specific heat of water = 5000 X 10 x 2.06 = 103.0 KJ

Q total = -2089 KJ

Entropy = -2089 / (273 + 15 ) = -7.25 KJ

The same amount of heat will be absrobed by surrounding so heat = 2089KJ

So entropy of surrounding = 2089 / 263= 7.94 KJ

so the entropy of universe = 7.94 -7.25 = 0.69 KJ (which is positive)

C) we may define the entropy as the degree of randomness.

However we we talk about the increase in entropy we should consdier the whole universe not the system only.

sytem here is the organism from microbes to large animals.

So if we talk about the whole universe necessarely the entropy is increasing and there is no violation of second law of thermodynamics.

This can be well correltaed with the first half of the question, where there was a decrease in entropy of sytem however overall an increase in entropy.