It has been proposed to use the thermal gradient of the ocean to drive a heat engine. Suppose that at a certain location the water temperature is \(22^\circ\)C at the ocean surface and \(4^{o}\)C at the ocean floor.
This is the Carnot efficiency, given by \begin{align} \eta &= 1-\frac{T_C}{T_H} \\ &= 1 - \frac{277}{295} \\ &\approx 6.1\% \end{align}
We start by finding out how much energy it takes to heat up water a gram by 18\(^\circ\)C. \begin{align} q &\equiv \frac{Q_{in}}{m} = c_p\Delta T \\ &= 4.2 \text{ J/g/K}\cdot 18\text{ K} \\ &= 75.6\text{ J/g} \end{align} We can then rearrange our equation for efficiency to solve for the mass of the water to find the mass of the water. We can use the value of the efficiency we found in part (a) using the Carnot efficiency equation. \begin{align} \eta & = \frac{W}{Q_{in}} \\ m &= \frac{P\Delta t}{c_p\Delta T \eta} \\ &= \frac{1\text{ GJ}}{75.6 \, \text{ J/g}\cdot 0.061} \\ &\approx 2\times 10^8 \, \text{g} \end{align} Thus the volume of water is \begin{align} V &= m/\rho \\ &= 2\times 10^8 \, \text{cm}^3 \\ &= 200 \, \text{m}^3 \end{align} Two hundred cubic meters per second is a pretty incredible amount of water to cool per second, but not entirely implausible.
It is very common for people to come up with schemes and inventions that violate the Second Law of Thermodynamics. These schemes consistently fail to work, and it is valuable to learn to evaluate whether a scheme will indeed violate the Second Law. In this problem, I'm going to ask you to skim through one or more recent articles, and identify and explain one claim that violates the Second Law. Not every article below contains a violation of the Second Law, so you may need to read more than one article.
The title of this article is enough to give you a strong hint that a violation of the Second Law (or less likely the First Law) is proposed. Limitless clean energy generally must have a source, and given that graphene is small, it seems unlikely to give us limitless energy.
There are several quotes that you could use from this article, but I think the simplest might be “An energy-harvesting circuit based on graphene could be incorporated into a chip to provide clean, limitless, low-voltage power for small devices or sensors.” From the context of the article, it is clear that the source of energy proposed is the ambient thermal environment, so this is a plan to extract thermal energy (cooling the environment) and convert it entirely into electrical work. This is by definition the “perfect heat engine” forbidden by the Kelvin formulation of the Second Law. This paragraph up to here would be a sufficient answer. You could also recognize that since the environment is getting cooled, and nothing is getting heated, the change in entropy of system plus environment is negative, violating the Second Law.
The title definitely suggests a planned violation of the Second Law, and it is clearly the intent of the authors. However, most of the paper attempts to skirt the issue. It returns, however, in the summary:“Our model provides a rigorous demonstration that continuous thermal power can be supplied by a Brownian particle at a single temperature while in thermal equilibrium, provided the same amount [emphasis theirs] of energypower is continuously dissipated in a resistor.”This statement is not entirely clear. If the resistor and the “generator” are at the same temperature, then this simply looks like a misuse of the term “work”. However, unless there is heat flow from the resistor back to the graphene, they will not remain at the same temperature, since dissipated power will heat up the resistor. If the power continues continually without returning via heating, the result will be a violation of the Second Law, as energy spontaneously flows from the cooler graphene to the hotter resistor.
This peer-reviewed paper lacks (most of) the “energy harvesting” language that was present in its preprint, making it less obvious that there is intent to violate the Second Law. The sentence quoted above is still present, however, with its implied violation of the Second Law. They will claim that this is not a violation of the Second Law, because both their “Brownian particle” and the resistor are at the same temperature. However, as I said above, the only way that will remain true is if the energy dissipated in the resistor returns to the Brownian particle.
Once you have identified a violation of the Second Law, please write up a short paragraph explaining why it violates the Second Law of Thermodynamics, including a direct quote demonstrating the error. Sometimes it is helpful to construct a scenario in which the proposed invention or observation could be used to heat up a system that is warmer using thermal energy extracted from a system that is cooler.
Hint: papers that claim not to violate the Second Law frequently do.