a graph between prssure P (along y-axis) and absolute temperature, T(along x-axis) for equal moles of two gases has been drawn . Given that volume of second gas is more than volume of first gas. Which of the following statement is correct?

Options

A. Slope of gas 1 is less than gas 2
B. Slope of gas 1 is more than gas 2
C. Both have some slopes
D. None of the above

Answer

To solve the problem, we need to analyze the relationship between pressure (P), volume (V), and temperature (T) for two gases using the ideal gas law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Number of moles (constant for both gases)
- \( R \) = Universal gas constant (constant)
- \( T \) = Absolute temperature

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**:
Since the number of moles (n) and the universal gas constant (R) are constant for both gases, we can express the relationship between pressure and temperature as:
\[ P = \frac{nRT}{V} \]
This shows that pressure is inversely proportional to volume for a given temperature.

2. **Rearranging the Equation**:
We can rearrange the equation to express pressure per unit temperature:
\[ \frac{P}{T} = \frac{nR}{V} \]
Here, \( \frac{P}{T} \) represents the slope of the graph of pressure (P) versus temperature (T).

3. **Identifying the Slopes**:
From the equation \( \frac{P}{T} = \frac{nR}{V} \), we can see that the slope of the graph for each gas is inversely proportional to its volume:
- For gas 1: \( \text{slope}_1 = \frac{nR}{V_1} \)
- For gas 2: \( \text{slope}_2 = \frac{nR}{V_2} \)

4. **Comparing the Volumes**:
According to the problem, the volume of the second gas (V2) is greater than the volume of the first gas (V1):
\[ V_2 > V_1 \]

5. **Analyzing the Slopes**:
Since the slopes are inversely proportional to the volumes:
- If \( V_2 > V_1 \), then \( \text{slope}_2 < \text{slope}_1 \).
This means that the slope of the graph for gas 1 is greater than the slope for gas 2.

6. **Conclusion**:
Therefore, the correct statement is:
\[ \text{slope of gas 1 is more than that of gas 2} \]

### Final Answer:
The correct option is: **B) Slope of gas 1 is more than that of gas 2.**