💨 Ideal Gas Law Calculator
Solve for pressure, volume, temperature, or moles using PV = nRT. Supports 7 common gases with process analysis.
📝 Configuration
Ideal Gas Law:
$PV = nRT$
$R = 8.314$ J/(mol·K)
$R_{spec} = R/M$ [J/(kg·K)]
Speed of sound:
$a = \sqrt{\gamma RT}$
Assumptions:
• No intermolecular forces
• Negligible molecular volume
• Valid at low P, high T
$PV = nRT$
$R = 8.314$ J/(mol·K)
$R_{spec} = R/M$ [J/(kg·K)]
Speed of sound:
$a = \sqrt{\gamma RT}$
Assumptions:
• No intermolecular forces
• Negligible molecular volume
• Valid at low P, high T
📊 Results & Visualization
Configure the inputs and click Calculate to see results.
📘 Calculation Methodology
Mathematical Model & Theory
The Ideal Gas Law relates the state variables of a hypothetical ideal gas. It is a good approximation for real gases under low pressures and high temperatures:
$$P V = n R_u T$$
$$R_u = 8.314 \text{ J/(mol·K)} \quad \text{(Universal gas constant)}$$
Worked Engineering Example
Problem Statement:
A 50-liter tank contains nitrogen gas at 25°C and 500 kPa. Find the number of moles of nitrogen in the tank.
Step-by-step Solution:
1. Convert units to SI base units:
$$V = 50 \text{ L} = 0.050 \text{ m}^3, \quad P = 500 \text{ kPa} = 500,000 \text{ Pa}$$ $$T = 25 + 273.15 = 298.15 \text{ K}$$ 2. Rearrange and solve Ideal Gas Law for moles ($n$):
$$n = \frac{P V}{R_u T} = \frac{500,000 \times 0.050}{8.314 \times 298.15} = 10.085 \text{ moles}$$
Final Result:
The tank contains 10.09 moles of nitrogen.
A 50-liter tank contains nitrogen gas at 25°C and 500 kPa. Find the number of moles of nitrogen in the tank.
Step-by-step Solution:
1. Convert units to SI base units:
$$V = 50 \text{ L} = 0.050 \text{ m}^3, \quad P = 500 \text{ kPa} = 500,000 \text{ Pa}$$ $$T = 25 + 273.15 = 298.15 \text{ K}$$ 2. Rearrange and solve Ideal Gas Law for moles ($n$):
$$n = \frac{P V}{R_u T} = \frac{500,000 \times 0.050}{8.314 \times 298.15} = 10.085 \text{ moles}$$
Final Result:
The tank contains 10.09 moles of nitrogen.