Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
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 law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below :

Options

A. Both A and R are correct but R is not 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 and R is the correct explanation of A

Answer

To solve the question regarding the Assertion A and Reason R, we will analyze both statements step by step.

### Step 1: Analyze Assertion A
Assertion A states: "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."

1. **Understanding the Terms**:
- dQ: Heat added to the system.
- dW: Work done on the system.
- dU: Change in internal energy of the system.

2. **First Law of Thermodynamics**:
The first law of thermodynamics can be expressed as:
\[ dU = dQ - dW \]
Rearranging this gives:
\[ dQ = dU + dW \]
If we consider work done on the system (which is usually taken as negative), the equation can be interpreted as:
\[ dQ = dU - dW \]
Therefore, Assertion A is **true**.

### Step 2: Analyze Reason R
Reason R states: "The first law of thermodynamics is based on the law of conservation of energy."

1. **Understanding the Law**:
The first law of thermodynamics indeed states that energy cannot be created or destroyed, only transformed from one form to another. This is the principle of conservation of energy.

2. **Conclusion**:
Since the first law of thermodynamics is fundamentally based on the conservation of energy, Reason R is also **true**.

### Step 3: Relationship Between Assertion and Reason
Now, we need to determine if Reason R is the correct explanation of Assertion A.

- Since both Assertion A and Reason R are true, and Reason R explains why Assertion A is valid (the relationship between heat, work, and internal energy is derived from the conservation of energy), we conclude that Reason R is indeed the explanation for Assertion A.

### Final Conclusion
Both Assertion A and Reason R are true, and Reason R is the correct explanation of Assertion A.

### Answer
Thus, the correct option is that both A and R are correct, and R is the correct explanation of A.

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