Which of the Maxwell distribution curves (obtained at different temperatures) shown in the following figure corresponds to the highest temperature of the gas ?

Options

A. A. A
B. B. B
C. C. C
D. D. D

Explanation

To determine which Maxwell distribution curve corresponds to the highest temperature of the gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Maxwell Distribution**: The Maxwell distribution describes the distribution of speeds of particles in a gas. Each curve in the figure represents the speed distribution at a different temperature.

2. **Recall the Relationship Between Temperature and Speed**: The root mean square (RMS) speed of gas molecules is given by the formula:
\[ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass of the gas. This indicates that the RMS speed is proportional to the square root of the temperature (\( v_{\text{rms}} \propto \sqrt{T} \)).

3. **Analyze the Curves**: In the given figure, each curve corresponds to a different temperature. The shape and position of the curves indicate the average speed of the gas molecules at those temperatures.

4. **Identify the Highest Speed Curve**: The curve that is furthest to the right on the x-axis (which represents speed) corresponds to the highest average speed of the gas molecules. Since speed is directly related to temperature, the curve with the highest average speed will correspond to the highest temperature.

5. **Determine the Correct Curve**: By comparing the curves, we can label them as follows:
- Curve A: \( U_A \)
- Curve B: \( U_B \)
- Curve C: \( U_C \)
- Curve D: \( U_D \)

From the analysis, we find that:
\[ U_D < U_C < U_B < U_A \]
This indicates that Curve A has the highest speed and therefore corresponds to the highest temperature.

6. **Conclusion**: The curve that corresponds to the highest temperature of the gas is Curve A.

### Final Answer:
The curve corresponding to the highest temperature of the gas is **Curve A**.