Question

In an average eruption of Old Faithful Geyser, 40,000 kg of water at 100°C flows into the Firehole river. The temperature of the river is 5°C. Assuming the volume of the water in the river is so large that its temperature does not change when the water from the geyser flows into it, calculate the total entropy change for the universe for each geyser eruption.

Answer 1

To calculate the total entropy change for the universe in each geyser eruption, we need to consider the entropy changes of the water from the geyser and the river. The heat transfer from the geyser is 950 J and the entropy change for the universe is also 950 J.

Step-by-step explanation:

To calculate the total entropy change for the universe in each geyser eruption, we need to consider the entropy changes of the water from the geyser and the river. The entropy change of a system is given by the equation ΔS = Q/T, where ΔS is the entropy change, Q is the heat transfer, and T is the temperature in Kelvin.

In the case of the water from the geyser, the initial temperature is 100°C, which is 373 K, and the final temperature is 5°C, which is 278 K. The entropy change for the water can be calculated as follows:

ΔS = Q/T

ΔS = Q/278

ΔS = -Q/373

-950 = -Q/373

Q = 950(373)/373

Q = 950 J

We need to multiply the heat transfer Q by -1 since it is defined as negative in the question. Therefore, the heat transfer from the geyser is 950 J.

Since the water in the river is so large that its temperature does not change, the entropy change for the river is 0.

The total entropy change for the universe is the sum of the entropy changes for the geyser and the river, which is ΔS_universe = ΔS_geyser + ΔS_river = 950 J + 0 = 950 J.