Combined Gas Law Calculator
Calculate thermodynamic processes for ideal gases: isothermal, isochoric, isobaric, and adiabatic
Calculate Thermodynamic Process
Gas type affects heat capacity values
Initial State
Final State (Enter ONE parameter to calculate others)
Constant in isothermal process
Calculation Results
Process formula:
Gas type: diatomic (Cv = 20.786 J/(mol·K), γ = 1.400)
First law: ΔU = Q - W
Example Calculation
Isobaric Process Example
Gas: Nitrogen (diatomic) in flexible container
Initial conditions: V₁ = 0.5 m³, T₁ = 250 K, p = 101.325 kPa
Final temperature: T₂ = 300 K
Amount of gas: n = 24.375 mol
Calculation Steps
1. V₂ = V₁ × T₂ / T₁ = 0.5 × 300 / 250 = 0.6 m³
2. W = p × ΔV = 101.325 × 0.1 = 10.133 kJ
3. ΔU = Cv × n × ΔT = 20.814 × 24.375 × 50 = 25.367 kJ
4. Q = ΔU + W = 25.367 + 10.133 = 35.500 kJ
Thermodynamic Processes
Isothermal
Temperature constant
p₁V₁ = p₂V₂
Isochoric
Volume constant
p₁/T₁ = p₂/T₂
Isobaric
Pressure constant
V₁/T₁ = V₂/T₂
Adiabatic
No heat exchange
p₁V₁^γ = p₂V₂^γ
Gas Law Tips
Use absolute temperature (Kelvin) for calculations
Heat capacity depends on gas molecular structure
Work is positive when gas expands
Internal energy depends only on temperature
Understanding Thermodynamic Processes
Combined Gas Law
The combined gas law relates pressure, volume, and temperature of an ideal gas. For a fixed amount of gas, the ratio pV/T remains constant throughout any process. This fundamental relationship allows us to predict how gases behave under different conditions.
First Law of Thermodynamics
ΔU = Q - W
- ΔU: Change in internal energy (J)
- Q: Heat absorbed by the system (J)
- W: Work done by the system (J)
Heat Capacities
Monoatomic Gas
Cv = (3/2)R = 12.47 J/(mol·K)
Cp = (5/2)R = 20.79 J/(mol·K)
γ = 5/3 = 1.67
Diatomic Gas
Cv = (5/2)R = 20.79 J/(mol·K)
Cp = (7/2)R = 29.10 J/(mol·K)
γ = 7/5 = 1.40
Polyatomic Gas
Cv = 3R = 24.94 J/(mol·K)
Cp = 4R = 33.26 J/(mol·K)
γ = 4/3 = 1.33
Process Characteristics
| Process | Constant | Formula | Work | Heat |
|---|---|---|---|---|
| Isothermal | Temperature | p₁V₁ = p₂V₂ | nRT ln(V₂/V₁) | W |
| Isochoric | Volume | p₁/T₁ = p₂/T₂ | 0 | CvnΔT |
| Isobaric | Pressure | V₁/T₁ = V₂/T₂ | pΔV | CpnΔT |
| Adiabatic | Heat (Q = 0) | p₁V₁^γ = p₂V₂^γ | -ΔU | 0 |