How Does Dropping a Hot Steel Rivet into a River Affect Entropy Change?

[Brewer]

Homework Statement

A shipyard worker drops a hot steel rivet (mass 125g, temperature 350°C) into a river at temperature 5°C, a distance of 30m below. Stating any assumptions you make, calculate the entropy change of the universe as a result of this event. (Specific heat capacity of steel ~ 0.4 J/(gK)

Homework Equations

I'm not entirely sure. Think I need Q = mcΔT. I also reckon I need an entropy equation like dS=dQ/T, but I don't think that's the correct form.

I think PE = mgh could also be used as well.

The Attempt at a Solution

Assumptions: no air resistance

So far I've used Q = mcΔT to work out the change in heat when the rivet is dropped in the water (-17.25 J) and PE = mgh to work out the change in energy as the rivet is dropped. Would the best bet from there be to say that dS = dU/T where U = Q + W, with W being the PE?

But as I don't have a constant temperature I must not be able to use dS=dU/T can I?

 

[anathema]

Thank you for your post. I would like to address your question and provide a solution to help you better understand the concept of entropy change in this scenario.

First, let's start with the assumptions you have made. Assuming no air resistance is a reasonable assumption in this scenario as it simplifies the calculation and does not significantly affect the final result.

Now, let's look at the equations you have mentioned. Q = mcΔT is the correct equation to use in this situation as it calculates the change in heat when the rivet is dropped into the water. However, we need to consider the specific heat capacity of steel, which is approximately 0.4 J/(gK). This means that for every 1 gram of steel, it requires 0.4 joules of energy to increase its temperature by 1 Kelvin.

Using this information, we can calculate the change in heat (Q) as follows:

Q = (0.125 kg) (0.4 J/(gK)) (350°C - 5°C) = 17.5 J

Next, let's consider the change in potential energy (PE) of the rivet as it falls into the water. As you have correctly mentioned, we can use the equation PE = mgh to calculate this change. However, in this scenario, we need to consider the change in height (h) as the rivet falls into the water. We know that the distance is 30m, but we need to consider the final height of the rivet in the water. Assuming the water is deep enough to fully submerge the rivet, we can consider the final height as 0 meters. Therefore, the change in potential energy is:

PE = (0.125 kg) (9.8 m/s^2) (30 m - 0 m) = 36.75 J

Now, we can calculate the change in internal energy (ΔU) as the sum of the changes in heat and potential energy:

ΔU = Q + PE = 17.5 J + 36.75 J = 54.25 J

Finally, we can calculate the change in entropy (ΔS) using the equation ΔS = ΔQ/T, where ΔQ is the change in heat and T is the final temperature of the system. In this scenario, the final temperature of the system is the temperature of the river,

 

[m2003]

I would like to clarify that there are a few things to consider when calculating the entropy change of the universe in this scenario. Firstly, the change in heat and potential energy are not the only factors that contribute to the entropy change. There are also changes in the surroundings, such as the water temperature increasing and the surrounding air temperature decreasing.

To accurately calculate the entropy change of the universe, we would need to consider all of these factors using the appropriate equations. This could include the heat transfer between the rivet and the water, the change in temperature of the water, and the change in temperature of the air. Additionally, the change in entropy of the surroundings would also need to be taken into account.

Furthermore, the assumption of no air resistance may not be entirely accurate as there will still be some air resistance present. This could affect the potential energy calculation and thus impact the overall entropy change.

In summary, to accurately calculate the entropy change of the universe in this scenario, we would need to consider all factors and use appropriate equations, taking into account any assumptions and potential limitations.