Ideal Gas Temperature Calculator
Free calculate temperature from pressure, volume, and number of moles using t = pv/(nr). Get instant, accurate results with our easy-to-use calculator.
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What is Ideal Gas Temperature?
Ideal gas temperature is calculated from the ideal gas law by rearranging PV = nRT to solve for temperature: T = PV/(nR).
Temperature in the ideal gas law must be in absolute units (Kelvin), as it represents the average kinetic energy of gas molecules. Zero Kelvin (absolute zero) represents the theoretical point where molecular motion stops.
This calculation is essential for understanding gas behavior, determining reaction conditions, and designing systems that depend on temperature-dependent gas properties.
Ideal Gas Temperature Formula
Where:
- • T = Temperature (K)
- • P = Pressure (Pa)
- • V = Volume (m³)
- • n = Number of moles (mol)
- • R = 8.314 J/(mol·K)
How to Calculate Ideal Gas Temperature
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1
Convert pressure to Pascals
Convert all pressure units to Pa for consistent calculations.
-
2
Convert volume to cubic meters
Convert liters or milliliters to m³ (1 L = 0.001 m³).
-
3
Apply the formula
Calculate T = PV / (nR) using R = 8.314 J/(mol·K).
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4
Convert to desired units
Convert Kelvin to Celsius (T°C = T K - 273.15) or Fahrenheit if needed.
Practical Examples
Example 1: Standard Conditions
Calculate the temperature when 1 mole of gas occupies 22.4 L at 1 atm pressure.
Solution:
P = 101,325 Pa, V = 0.0224 m³, n = 1 mol
T = (101,325 × 0.0224) / (1 × 8.314)
T = 273.15 K = 0°C (standard temperature!)
Example 2: Compressed Gas
A 0.5 L container holds 0.2 moles of gas at 500 kPa. What is the temperature?
Solution:
P = 500,000 Pa, V = 0.0005 m³, n = 0.2 mol
T = (500,000 × 0.0005) / (0.2 × 8.314)
T = 150.4 K = -122.8°C
Applications
Chemical Reactions
Determining reaction temperatures for gas-phase reactions and understanding temperature effects on equilibrium.
Process Control
Monitoring and controlling temperatures in industrial gas processes and reactors.
Automotive
Engine temperature calculations, tire pressure-temperature relationships, and airbag systems.
Aerospace
Cabin temperature control, gas storage systems, and altitude-temperature relationships.
Frequently Asked Questions
Why must temperature be in Kelvin?
The gas constant R is defined using Kelvin. Temperature in the ideal gas law represents molecular kinetic energy, which is zero at absolute zero (0 K), not at 0°C.
What happens if I use Celsius instead of Kelvin?
You'll get incorrect results. For example, at 0°C, using Celsius would give T = 0, making the calculation invalid. Always convert to Kelvin first.
Can temperature be negative in Kelvin?
No, absolute zero (0 K) is the lowest possible temperature. Negative Kelvin temperatures are physically impossible for ideal gases.
How does pressure affect temperature at constant volume?
At constant volume and moles, temperature is directly proportional to pressure (Gay-Lussac's law). Doubling pressure doubles temperature.