It is nearly a very impossible thing for heat to move by itself from a temperature which is lower in temperature and the reservoir which is a higher temperature that is reservoir. That is we can say that the transfer of heat and we can only occur spontaneously in the temperature of direction decrease. For example we cannot construct a refrigerator that can operate without any input work.
That is, the transfer of heat can only occur spontaneously in the temperature direction which decreases.
The theorem of clausius in 1855 states that for a thermodynamic system that is the heat engine or even heat pump exchanging heat with external reservoirs and thermodynamics undergoing of a cycle
Statement Which is of Celcius
This is the amount of infinitesimal heat which is absorbed by the system from the reservoir and is the external temperature of a reservoir that is surroundings at a particular instant in time. The integral which is closed is carried out along a process of thermodynamic process path from the initial/final state to the same initial/final state. In principal, the closed integral which can start and end at a point which is arbitrary along the path.
If there are multiple reservoirs with different temperatures then inequality of Clausius reads the following:
In the case of a process which is reversible, the holds of equality. The case which is reversible is used to introduce the function of the state which is known as entropy. This is because in a process which is cyclic the variation of a state function is zero. In other words we can say that the Clausius statement tells that it is impossible to construct a device whose effects are sole effect is the transfer of heat from a reservoir which is cool to a hot reservoir. Equivalently the spontaneously flows of heat from a hot body to a cooler one.
The generalization is clausius inequality.
History of Clausius theorem
The theorem of Clausius is an explanation of mathematics of the thermodynamics second law. It was developed by Rudolf Clausius who explained intended the relationship which is between the flow of heat flow in a system and the entropy of the system and its surroundings. The development of Clausius in his efforts to explain entropy and it is quantitatively defined. In items which are direct terms the theorem gives us a way to determine if a process of cyclical is irreversible or reversible. The theorem of Clausius provides a formula which is quantitative for understanding the second law.
Clausius was one of the first to work on the idea of entropy and it is even responsible for giving it that name to the theorem. What is now known as the theorem of Clausius was first published in 1862 in Clausius' On the Application of the Theorem of the transformation Equivalence to Interior Work". Sought Clausius to show a proportional relationship which is between entropy and the energy flow by heating defined by the symbol δQ into a system.
In a system the energy of heat can be transformed into work, and the work can be transformed into heat through a process which is cyclical. Writes the Clausius that The algebraic sum of all the transformations which is occurring in a process which is cyclical can only be less than zero, or, as a case of extreme equal to nothing. In other words we can say that the equation is given below:
Clause Statement of Second Law of Thermodynamics
In 1850 Here we can see that one of the earliest statements of the thermodynamics Second Law was made by R. Clausius. He stated the following mentioned in the next line.
“It is very impossible to construct a device that operates on a cycle and whose effect is the heat transfer from a body which was cooler to a hotter one.
Heat spontaneously cannot flow from the system of cold to the hot system without external work being performed on the system. This is exactly what heat pumps and refrigerators accomplish. In a heat flow or the refrigerator from the body which is cold to hot, but only when forced by an external work, the refrigerators are driven by motors which are electric and require work from their surroundings to operate.
The Clausius statement of law states the following:
Heat can be transferred from a body which is cooler to a body which is hotter if other effects accomplishing the heat transfer occur within the surrounding or system or both. Air conditioners or AC and refrigerators are devices which are supposed to transfer heat from a cool space to its hot surroundings. But in both the cases they need power input. The statement which is of Clausius says that an air conditioner won't cool a room without power input.
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Kelvin-planck Statement of the Second Law
A engine or a heat engine must reject some energy to sink the heat in order to run a cycle. That is no engine of heat that can convert all the heat it received from a temperature of high source to work. It is the basis for the planks of Kelvin statement of the thermodynamics second law which is given as:
The plank Kelvin statement which puts forward the idea that no engine of heat can have 100 percent efficiency. It must exchange the low heat temperature sink of heat as well as a high-temperature source to complete the cycle of thermodynamics.