Question

According to the principle of method of mixtures, if A and B are the net heat lost and net heat gain respectively, then

• A. \(A > B\)
• B. \(A < B\)
• C. A = B
• D. None of these

Answer 1

The Correct Option is C

The principle of the method of mixtures is a concept in thermodynamics that deals with the thermal equilibrium achieved when a hot object is mixed with a cold object. This principle is based on the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred. When two objects are mixed, the net heat lost by the hot object is equal to the net heat gained by the cold object until thermal equilibrium is reached.

In this context, if we denote:

• \(A\) as the net heat lost by the hot object
• \(B\) as the net heat gained by the cold object

According to the principle of conservation of energy, the heat lost by the hot object must equal the heat gained by the cold object, provided no heat is lost to the surroundings. Therefore, mathematically, this is expressed as:

\[A = B\]

This equation shows that the total heat lost by the hot substance is transferred entirely to the cold substance.

Thus, the correct answer is \(A = B\).

Answer 2

Concept: According to the principle of method of mixtures, in an ideal setup with no loss of heat to the surroundings, the heat lost by the hot body is equal to the heat gained by the cold body.

Let:

• A = Net heat lost
• B = Net heat gained

Then, according to the principle:

A = B

Final Answer: A = B