The graph which represents the variation of mean kinetic energy of moleules with temperature `""^(@)C` is ?

Options

A.
B.
C.
D.

Explanation

To solve the problem of finding the graph that represents the variation of mean kinetic energy of molecules with temperature in degrees Celsius, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The mean kinetic energy (E) of molecules is related to the temperature (T) of the gas. The formula for mean kinetic energy is given by:
\[ E = \frac{F}{2} k T \]
where \( F \) is the degrees of freedom, \( k \) is the Boltzmann constant, and \( T \) is the temperature in Kelvin.

2. **Convert Celsius to Kelvin**: Since the temperature is given in degrees Celsius, we need to convert it to Kelvin. The conversion is done using the formula:
\[ T(K) = T(°C) + 273 \]

3. **Substitute the Temperature**: Substitute the expression for \( T \) into the kinetic energy equation:
\[ E = \frac{F}{2} k (T(°C) + 273) \]
This can be expanded to:
\[ E = \frac{F}{2} k T(°C) + \frac{F}{2} k \cdot 273 \]

4. **Identify the Linear Form**: The equation can be rearranged into the form of a linear equation \( Y = MX + C \):
- Here, \( Y \) represents the mean kinetic energy \( E \),
- \( X \) represents the temperature in degrees Celsius \( T(°C) \),
- \( M \) (the slope) is \( \frac{F}{2} k \),
- \( C \) (the y-intercept) is \( \frac{F}{2} k \cdot 273 \).

5. **Graph Characteristics**: Since the slope \( M \) is positive, the graph will be a straight line that rises as the temperature increases. The y-intercept \( C \) indicates that even at 0°C, there is a positive value for mean kinetic energy.

6. **Conclusion**: The graph representing the variation of mean kinetic energy of molecules with temperature in degrees Celsius will be a straight line with a positive slope, starting from a positive y-intercept.

### Final Answer:
The correct graph is a straight line with a positive slope, indicating that as the temperature increases, the mean kinetic energy of the molecules also increases.