# Maxwell-Boltzmann Distribution AI Agent Connect

> Calculate gas particle speed distributions and statistical characteristics.

## Overview
- **Category:** science
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_BU9efmHEqr7phaJUP5L27ypqV7GsEb1pRC2y6zvE/ai-agent-connect
- **Tags:** physics, gas-laws, statistics, thermodynamics, molecular-dynamics

## Description

This MCP server provides tools to calculate the Maxwell-Boltzmann speed distribution for ideal gases. It allows AI agents to determine characteristic speeds such as most probable, average, and root-mean-square speeds based on temperature and molecular mass. Users can also generate probability density values for specific speeds or retrieve data points for plotting the full distribution curve using `get_distribution_curve` and `get_speed_statistics`.

## Tools

### get_distribution_curve
Generate data points for the speed distribution curve

### get_distribution_summary
Provide a textual summary of the distribution characteristics

### get_probability_density
Calculate the probability density for a specific speed

### get_speed_statistics
Retrieve the primary characteristic speeds of a gas

## Prompt Examples

**Prompt:** 
```
What are the characteristic speeds for Helium at 300K?
```

**Response:** 
```
For Helium at 300K, the most probable speed is approximately 1260 m/s, the average speed is 1560 m/s, and the rms speed is 1715 m/s.
```

**Prompt:** 
```
Calculate the probability density for a speed of 500 m/s for a gas with mass 0.028 kg/mol at 273K.
```

**Response:** 
```
The probability density for a speed of 500 m/s under these conditions is 0.00045.
```

**Prompt:** 
```
Summarize how temperature affects the distribution for a gas with mass 0.044 kg/mol.
```

**Response:** 
```
Increasing the temperature increases the spread factor and shifts the peak speed to a higher value.
```

## Frequently Asked Questions

**What inputs are required for the calculations?**
You must provide the absolute temperature in Kelvin and the molecular mass of the gas in kilograms.

**Can I get the full curve data for plotting?**
Yes, you can use the `get_distribution_curve` tool to retrieve a set of speed and density data points.

**What kind of speed statistics are provided?**
The `get_speed_statistics` tool provides the most probable speed, the average speed, and the root-mean-square (rms) speed.