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 determining 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 temperature (T) through the formula:
\[ E = \frac{F}{2} k T \]
where \( F \) is the degrees of freedom and \( k \) is the Boltzmann constant.

2. **Convert Temperature to Kelvin**: Since the formula uses temperature in Kelvin, we need to convert the temperature from degrees Celsius to Kelvin:
\[ T(K) = T(°C) + 273 \]

3. **Substitute the Temperature**: Substitute the temperature in Kelvin into the kinetic energy formula:
\[ E = \frac{F}{2} k (T + 273) \]
This can be expanded to:
\[ E = \frac{F}{2} k T + \frac{F}{2} k \cdot 273 \]

4. **Identify the Linear Equation**: The equation now resembles the linear form \( y = mx + c \), where:
- \( y \) corresponds to \( E \)
- \( x \) corresponds to \( T \)
- \( m \) (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 of \( E \) versus \( T \) will be a straight line with a positive slope. The y-intercept will also be positive, indicating that the line crosses the y-axis above zero.

6. **Draw the Graph**: On a graph where the x-axis represents temperature (in °C) and the y-axis represents mean kinetic energy (E), the line will start from a positive intercept and rise as the temperature increases.

7. **Select the Correct Option**: Based on the characteristics of the graph derived, we can conclude that the correct option is the one that shows a straight line with a positive slope intersecting the y-axis above zero.

### Final Answer:
The graph that represents the variation of mean kinetic energy of molecules with temperature in degrees Celsius is a straight line with a positive slope and a positive y-intercept.

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