๐จ Ideal Gas Calculator
Equation of state, isothermal/adiabatic/polytropic processes, and specific heat properties for ideal gases.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Thermodynamics
๐ Solver Telemetry
โ ACTIVE
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โก Solves
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๐ฆ Fortran Code
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๐
Released
Feb 2024
โฑ๏ธ Latency
< 1 ms
Ideal Gas Law Solver
Solve for any unknown state variable ($P, V, T, n$) by selecting the target variable, picking a gas preset, and providing the remaining known properties:
- Equation of State: $PV = nRT$ where $R = 8.314\text{ J/(molยทK)}$.
- Gas preset: Determines molecular weight $M$ and specific heat ratio $\gamma$.
- Apparatus Animation: Shows molecular kinetic velocity changes with temperature $T$.
- PV curves: Visualizes isothermal and isentropic paths starting from the calculated state.
๐ Configuration
Ideal Gas Law:
$PV = nRT$
$R = 8.314$ J/(molยทK)
$R_{spec} = R/M$ [J/(kgยทK)]
Speed of sound:
$a = \sqrt{\gamma RT}$
Assumptions:
โข No intermolecular forces
โข Negligible molecular volume
โข Valid at low P, high T
$PV = nRT$
$R = 8.314$ J/(molยทK)
$R_{spec} = R/M$ [J/(kgยทK)]
Speed of sound:
$a = \sqrt{\gamma RT}$
Assumptions:
โข No intermolecular forces
โข Negligible molecular volume
โข Valid at low P, high T
๐ Results & Visualization
Configure the inputs and click Calculate to see results.
๐ 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:
$$P V = n R_u T$$
$$R_u = 8.314 \text{ J/(molยทK)} \quad \text{(Universal gas constant)}$$
Assumptions & Boundary Conditions:
- The volume occupied by the gas molecules themselves is negligible compared to the total volume of the container.
- The attractive or repulsive intermolecular forces between gas molecules are negligible.
- Collisions between molecules and container walls are perfectly elastic (no kinetic energy loss).
- The gas is in local thermodynamic equilibrium.
Academic References:
- Cengel, Y. A., & Boles, M. A. (2015). Thermodynamics: An Engineering Approach (8th ed.). McGraw-Hill.
- Moran, M. J., Shapiro, H. N., Boettner, D. D., & Bailey, M. B. (2014). Fundamentals of Engineering Thermodynamics (8th ed.). John Wiley & Sons.
Worked Engineering Example
Problem Statement:
A 50-liter tank contains nitrogen gas at 25ยฐC 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 25ยฐC 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.