A : Number of air molecules in a room in winter is more than the number of molecules in the same room in summer.
R : At a given pressure and volume, the number of molecules of a given mass of a gas is directly proportional to the absolute temperature.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then Mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To solve the problem, we need to analyze the assertion (A) and the reason (R) given in the question.

### Step 1: Understand the Assertion (A)
The assertion states that the number of air molecules in a room in winter is more than the number of molecules in the same room in summer.

### Step 2: Understand the Reason (R)
The reason states that at a given pressure and volume, the number of molecules of a given mass of a gas is directly proportional to the absolute temperature.

### Step 3: Analyze the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles (or molecules)
- \( R \) = universal gas constant
- \( T \) = absolute temperature in Kelvin

### Step 4: Consider Conditions in Winter and Summer
Assuming the pressure \( P \) and volume \( V \) of the room remain constant, we can rearrange the ideal gas equation to express the number of moles:
\[ n = \frac{PV}{RT} \]
From this equation, we see that \( n \) (the number of moles) is inversely proportional to the temperature \( T \) when pressure and volume are constant.

### Step 5: Compare Temperatures in Winter and Summer
In winter, the temperature \( T \) is lower than in summer. Since \( n \) is inversely proportional to \( T \):
- Lower \( T \) (winter) → Higher \( n \) (more molecules)
- Higher \( T \) (summer) → Lower \( n \) (fewer molecules)

### Step 6: Conclusion on Assertion
Thus, the assertion (A) is correct: there are more air molecules in the room in winter than in summer.

### Step 7: Conclusion on Reason
Now, let's analyze the reason (R). The reason states that the number of molecules is directly proportional to the absolute temperature, which is incorrect. The number of molecules is actually inversely proportional to the temperature.

### Final Conclusion
- Assertion (A) is true.
- Reason (R) is false.

Therefore, the correct answer is that the assertion is true, and the reason is false.

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