Question

According to the law of entropy, which of the following statements is true?
A. heat always flows spontaneously from a colder body to a hotter one
B. every natural system will tend towards lower entropy
C. heat lost by one object must be gained by another
D. the specific heat of a substance cannot exceed a certain value
E. every natural system will tend towards disorder.

Answer 1

To solve this question, we need to understand the definition of the concept of Entropy.

Entropy is an extensive property of a thermodynamic system which represents the randomness of a system and this is equal to the ratio of the change in the heat in the system at a particular temperature in kelvin.
Entropy, $S = \dfrac{{\Delta Q}}{T}$ where T is the temperature of the system in kelvin (K)

Complete step-by-step answer:
The concept of entropy arises from the fact that the systems in the real world are irreversible, which means after a system is taken through a process, it is not possible to return the system to its exact same form as before, because of the existence of a quantity called entropy. The second law of thermodynamics, also called the law of entropy gives us the clear understanding of this, which says:
The total entropy of an isolated system is always increasing.
Now, let us examine all the statements to view their validity.

Statement – A: heat always flows spontaneously from a colder body to a hotter one
The alternative form of the second law of thermodynamics also, states that –
Heat can never flow on itself, from a cold body to a hot body.
This arises due to the fact that the second law of thermodynamics, which says that entropy is always increasing. Hence,
Statement – A is wrong.

Statement – B: every natural system will tend towards lower entropy
The second law of thermodynamics clearly, states that the entropy of any system is always increasing. So, obviously, this statement is a clear negation of the second law.
Statement – B is wrong.

Statement – C: heat lost by one object must be gained by another
The heat lost by one system can be gained by another only, if the process in which the heat transfer takes place, is reversible, which is not a possibility given that the second law rules that a reversible process cannot take place in the real world due to the entropy, which increases constantly.
Thus, all systems are irreversible and this statement cannot be true.
Statement – C is wrong.

Statement – D: the specific heat of a substance cannot exceed a certain value
The specific heat of a substance is defined as the amount of heat added or removed from a system of unit mass per unit change in temperature.
If $\Delta Q$ is the change in heat energy in a system of mass $m$ and the temperature change is $\Delta T$ , the specific heat is given by :
$c = \dfrac{{\Delta Q}}{{m\Delta T}}$
We also, know that entropy is calculated as,
$S = \dfrac{{\Delta Q}}{T}$
Since, the entropy of a system is constantly increasing, there is no upper limit that the ratio $\dfrac{{\Delta Q}}{{\Delta T}}$ can take, and hence, the specific heat capacity can take, literally, any value.
Statement – D is wrong.

Statement – E: every natural system will tend towards disorder.
Entropy is the measure of randomness or disorder in the system. The second law states that every natural system has an increasing value of entropy. Hence, it can be concluded that every system in the real world tends to move towards disorder or randomness.
Hence, this statement is correct.

Only Statement-E is the correct statement.

Note: The fact that entropy is always increasing for a system gave rise to great number of concepts called refrigeration and several heat engines like Carnot cycle, Otto cycle, Rankine and Diesel cycles which work on the fact that :
To transfer the heat from cold body to hot body, the work should be performed on the system (W is positive) and when the heat is transferred from hot body to cold body, it happens automatically, and the system performs work (W is negative).