For a closed container containing 10 moles of an ideal gas, at constant pressure of `0.82` atm, which graph correctly represent, variation of log V us log T where volume is in litre and temp. in kelvin :

Options

A.
B.
C.
D.

Explanation

To solve the problem of determining which graph correctly represents the variation of log V versus log T for a closed container containing 10 moles of an ideal gas at a constant pressure of 0.82 atm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature.

2. **Rearrange the Ideal Gas Law**:
We need to express volume \( V \) in terms of temperature \( T \). Rearranging the ideal gas law gives:
\[ V = \frac{nRT}{P} \]

3. **Take the Logarithm of Both Sides**:
To find the relationship between log V and log T, we take the logarithm of both sides:
\[ \log V = \log\left(\frac{nRT}{P}\right) \]
This can be expanded using properties of logarithms:
\[ \log V = \log(nR) + \log T - \log P \]

4. **Identify Constants**:
Since \( n \) (10 moles), \( R \) (0.082 atm·L/(mol·K)), and \( P \) (0.82 atm) are constants, we can combine them:
\[ \log V = \log T + \text{constant} \]
Here, the constant is \( \log(nR/P) \).

5. **Determine the Slope and Intercept**:
The equation can be rewritten in the form:
\[ \log V = \log T + \text{constant} \]
This indicates that the slope (m) is 1, and the y-intercept (C) is the constant value \( \log(nR/P) \).

6. **Calculate the Constant**:
We can calculate the constant:
\[ n = 10, \quad R = 0.082, \quad P = 0.82 \]
\[ \log\left(\frac{nR}{P}\right) = \log\left(\frac{10 \times 0.082}{0.82}\right) = \log(1) = 0 \]
Thus, the y-intercept is 0.

7. **Final Equation**:
Therefore, we have:
\[ \log V = \log T \]
This indicates a linear relationship with a slope of 1 and a y-intercept of 0.

8. **Graph Interpretation**:
The graph of \( \log V \) versus \( \log T \) will be a straight line passing through the origin (0,0) with a slope of 1, which corresponds to an angle of 45 degrees.

### Conclusion:
The correct graph that represents the variation of log V versus log T is the one that shows a straight line with a slope of 1 and passes through the origin.