# Can the energy transferred to a system as heat be saved completely as mechanical energy of the system?

If energy is transferred to a system (as heat or work) and there is no transfer of energy from this system, then the energy transferred to the system will be saved as one of the forms of energy of the system i.e. increase the energy of the system (which may be thermal energy, mechanical energy, chemical energy etc). If the energy transfer was as work then this can be completely be saved as either mechanical energy of the system or thermal energy of the system (we won't consider other energy of the system). But if the energy transfer was as heat then this can be saved completely as the thermal energy of the system but the energy transferred cannot be completely be saved as mechanical energy. Is this the case or can the complete energy transferred to the system as heat can also be saved as mechanical energy of the system? (As mechanical energy can be completely be changed to work easily).

• No offence 1, but what does the second law say? No offence 2, paragraphs would make it easy to read.
– user176049
Nov 21, 2017 at 12:38
• It depends on what you define as being included in your system. Nov 21, 2017 at 16:41

Each type of energy is associated with a certain amount of entropy. For example, the mechanical energy, electricity, and laser light have low entropy. Other types of energy are not "entropy free", especially the heat energy.

Entropy can increase, but cannot decrease during the process of conversion of one type of energy to another. You can convert one low-entropy energy type to another and back with minimal technical losses, because this process does not conceptually change the entropy of the system. For example, you can convert electricity to the mechanical energy and back with little losses, such in hybrid electric cars.

You can also convert a low-entropy energy to a high-entropy energy. For example, an electric heater converts electricity to heat 100%. The same way friction converts the mechanical energy to heat 100%.

However, you cannot convert 100% of a high-entropy energy, such as heat, to a low-entropy energy, such as electricity or mechanical energy. This would contradict the law of the entropy increase. The total amount of entropy in the system must not decrease. For this reason, the efficiency of such a conversion would be limited. For example, the efficiency of an internal combustion engine in cars is only about 40% with the rest just heating the outside air.

So, to answer your question, we can store the heat energy in an insulated heated object, but we cannot completely convert heat to the mechanical energy. Accorging to the Carnot's theorem of thermodynamics, the maximum efficiency of a heat engine is:

$$\eta=1-\dfrac{T_c}{T_h}$$

Where $T_c$ is the temperature of the environment and $T_h$ is the temperature of the heater.

• Canceled the anonymous downvote. But some clarification in your answer is required. For e.g. what is the entropy associated with "... mechanical energy, electricity, and laser light..."? Also the statement "... you cannot convert 100% of a high-entropy energy, such as heat, to a low-entropy energy..." will be correct only when you add that no increase in entropy somewhere else results. For the same reason "... total amount of entropy in the system must not decrease..." must have "universe" instead of "system".
– Deep
Nov 22, 2017 at 5:06
• @Deep Thanks so much! Of course, my answer is not a physical thesis, but simply phrased in practical terms for a layman to understand. I agree with all your points and believe that my answer doesn't contradict any of them. My main point is that the mechanical energy, electricity, and coherent light are the sources of energy that are essentially entropy free, so ideally you could convert one to another with no loss. However, in reality, there always is friction and electrical resistance, and the light coherence is limited, so some entropy increase does happen during the conversion. [Continued] Nov 22, 2017 at 5:32
• Can you give a reference for "Each type of energy is associated with a certain amount of entropy.", or at least explain where this association is supposed to come from in standard statistical physics? Nov 23, 2017 at 20:09
• The point is that entropy is the number of microstates associated to a particular macrostate of a statistical system. Just having a gazillion particles is not enough, you need to not know and not care in what state exactly each particle is in to have a notion of entropy. The only sense in which I can see "types of energy" being associated to low/high entropy is whether increasing that type of energy for the macrostate increases the number of available microstates or not, Nov 23, 2017 at 20:56
• but I haven't really seen this distinction being made in statistical mechanics, and it is not obvious to me the correspondence between the types of energy and low/high entropy is as you say. In particular, heat is not a state function - between two states with fixed entropy differences there are processes which take more or less heat than the others to complete, yet the resulting entropy difference remains the same, so I can't even confirm the intuitively sort-of plausible association of heat energy to high entropy. Nov 23, 2017 at 20:56