Engines, compressors and refrigerators run gases through combinations of these basic processes. Knowing the work and heat in each step tells how much useful energy a cycle can deliver.
How to use the Thermodynamic Processes Calculator
- Process
- Gas
- Heat capacity ratio γ
- Initial pressure p₁
- Initial volume V₁
- Initial temperature T₁
- Final volume V₂
- Final pressure p₂
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the process and the gas, enter the initial pressure, volume and temperature, and the final value that defines the process.
Tips
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.
Common mistakes to avoid
- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).
Inputs explained
| Field | What to enter |
|---|---|
| Process | Choose one: Isobaric (constant p), Isochoric (constant V), Isothermal (constant T), Adiabatic / isentropic … |
| Gas | Choose one: Air, Nitrogen N₂, Oxygen O₂, Hydrogen H₂ … |
| Heat capacity ratio γ | A number |
| Initial pressure p₁ | Units: kPa, Pa, bar, atm, psi, MPa |
| Initial volume V₁ | Units: L, m³, mL, ft³ |
| Initial temperature T₁ | Units: K, °C, °F |
| Final volume V₂ | Units: L, m³, mL, ft³ |
| Final pressure p₂ | Units: kPa, Pa, bar, atm, psi, MPa |
What each result means
- Amount of gas n = [Initial pressure p₁]×[Initial volume V₁]÷(8.314462618×[Initial temperature T₁])
- Final pressure = [p2]
- Final volume = [V2]
- Final temperature = [T2]
- Change in internal energy ΔU = [Amount of gas n]×[cv]×([T2] – [Initial temperature T₁])
- Change in entropy ΔS = [Amount of gas n]×[cv]×ln([T2]÷[Initial temperature T₁]) + [Amount of gas n]×8.314462618×ln([V2]÷[Initial volume V₁])
Formula
Combined gas law: p₁V₁/T₁ = p₂V₂/T₂ · Isothermal: W = nRT·ln(V₂/V₁) · Adiabatic: pV^γ = constΔU = n·c_v·ΔT, Q = ΔU + W, ΔS = n·c_v·ln(T₂/T₁) + n·R·ln(V₂/V₁)Worked example
Inputs — Process: General (combined gas law); Gas: Air; Initial pressure p₁: 101.325 kPa; Initial volume V₁: 10 L; Initial temperature T₁: 293.15 K; Final volume V₂: 5 L; Final pressure p₂: 250 kPa.
Results — Amount of gas n = 0.41571 mol; Final pressure = 250 kPa; Final volume = 5 L; Final temperature = 361.64569 K; Change in internal energy ΔU = 591.875 J; Change in entropy ΔS = -0.58136 J/K.
Key terms
- Adiabatic
- Without heat exchange.
Frequently asked questions
What is the combined gas law?
p₁V₁/T₁ = p₂V₂/T₂ for a fixed amount of gas.
Why is work undefined for a general process?
It depends on the path, not just the end states.
Why does adiabatic compression heat the gas?
Work done on the gas raises its internal energy.
What is γ for air?
About 1.4.
What formula does the Thermodynamic Processes Calculator use?
Combined gas law: p₁V₁/T₁ = p₂V₂/T₂ · Isothermal: W = nRT·ln(V₂/V₁) · Adiabatic: pV^γ = const.