A steel cylinder of 8 litres capacity contain hydrogen gas at 12atm pressure. At the same temperature how many cycle tubes of 4 litres capacity at 2 atm can be filled up with this gas.
(A) 12, B) 48, ( c) 5, (D) 10

Answer

To solve the problem, we will use the ideal gas law principle, specifically the relationship between pressure, volume, and the number of moles of gas at constant temperature.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Volume of the steel cylinder (V1) = 8 liters
- Pressure in the steel cylinder (P1) = 12 atm
- Volume of one cycle tube (V2) = 4 liters
- Pressure in one cycle tube (P2) = 2 atm

2. **Use the Ideal Gas Law Relation:**
Since the temperature is constant, we can use the relationship:
\[ P_1 \times V_1 = n \times P_2 \times V_2 \]
where \( n \) is the number of cycle tubes that can be filled.

3. **Substitute the Values:**
Plugging in the values we have:
\[ 12 \, \text{atm} \times 8 \, \text{liters} = n \times 2 \, \text{atm} \times 4 \, \text{liters} \]

4. **Calculate the Left Side:**
\[ 12 \times 8 = 96 \, \text{atm-liters} \]

5. **Set Up the Equation:**
\[ 96 = n \times (2 \times 4) \]
Simplifying the right side:
\[ 2 \times 4 = 8 \]
Therefore, the equation becomes:
\[ 96 = n \times 8 \]

6. **Solve for n:**
\[ n = \frac{96}{8} = 12 \]

7. **Conclusion:**
The number of cycle tubes that can be filled is \( n = 12 \).

### Final Answer:
The correct option is (A) 12.

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