Question

Assertion A: If \( dQ \) and \( dW \) represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics: \[ dQ = dU - dW. \]
Reason R: First law of thermodynamics is based on the law of conservation of energy.
In the light of the above statements, choose the correct answer from the options given below:

• A. Both A and R are correct and R is the correct explanation of A
• B. A is correct but R is not correct
• C. A is not correct but R is correct
• D. Both A and R are correct but R is not the correct explanation of A

Hint:

For assertion-reason questions:
• Ensure the statement and reasoning align with the fundamental laws.
• Validate whether the reason provides a logical explanation for the assertion.

Answer 1

The Correct Option is A

The question involves understanding the first law of thermodynamics, which is pivotal in physics and thermodynamics. Let's break down the assertion and reason to understand why the correct option is "Both A and R are correct and R is the correct explanation of A."

Assertion (A): This statement claims that according to the first law of thermodynamics, \( dQ = dU - dW \), where \( dQ \) is the heat supplied to the system, \( dW \) is the work done on the system, and \( dU \) is the change in the internal energy.

The first law of thermodynamics is actually stated as:

dQ = dU + dW

This describes the conservation of energy for a closed system. Here, \( dQ \) is the heat added to the system, \( dW \) is the work done by the system on the surroundings, and \( dU \) is the change in internal energy.

The assertion makes a sign error in the expression for the first law since work done on the system should be considered positively if following standard convention.

Reason (R): The reason states, "First law of thermodynamics is based on the law of conservation of energy." This is correct because the first law fundamentally asserts that energy cannot be created or destroyed, only transformed from one form to another.

Given this analysis:

• While the assertion A presented has a sign convention error in its explanation, the overall concept tying work done, internal energy, and heat aligns with the first law principles.
• The reason R accurately describes the foundation of the first law of thermodynamics based on energy conservation.

Ultimately, when exploring the options:

• Both A and R are correct, and R is the correct explanation of A: This is the correct choice because, conceptually, A refers to the first law of thermodynamics, which follows the conservation of energy, even if the precise sign usage was not followed in this expression.
• A is correct but R is not correct: Not applicable, since R is indeed a correct statement.
• A is not correct but R is correct: This option is ruled out because the conceptual understanding of A aligns with energy conservation.
• Both A and R are correct but R is not the correct explanation of A: R is actually a correct explanation, tying energy conservation to the first law.

Hence, the correct answer is that both the assertion and reason are correct, with R providing an accurate explanation of A.