Quick answer
For an ideal gas, isothermal work is W = nRT ln(V₂/V₁), isobaric work P(V₂ − V₁), isochoric work 0, and adiabatic T₂ = T₁(V₁/V₂)^(γ−1). One mole of a monatomic gas doubling in volume at 300 K does 1,728.9 J of work.
Choose a process and gas type, then enter the amount, temperature and volumes. The calculator returns work, change in internal energy, heat added and final temperature. Use this thermodynamic processes calculator to check your own figures.
Related tools: Specific Heat Calculator: Specific heat capacity or heat required from Q = m c ΔT. EER Calculator: Energy efficiency ratio of an air conditioner and its COP equivalent. Heat Pump COP Calculator: Coefficient of performance from heat output and power input, or the Carnot limit.
How to use the Thermodynamic Processes Calculator
- Choose process: Isothermal, Isobaric, Isochoric and Adiabatic.
- Choose gas: Monatomic (e.g. helium) and Diatomic (e.g. air, N₂).
- Enter amount of gas (mol) (above 0).
- Enter initial temperature (K) (above 0).
- Enter initial volume (m³) (above 0).
- Optionally, enter final volume (m³) (above 0).
- Optionally, enter final temperature (isochoric) (K) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Process | Choose one: Isothermal; Isobaric; Isochoric; Adiabatic | Starts at Isothermal |
| Gas | Choose one: Monatomic (e.g. helium); Diatomic (e.g. air, N₂) | Starts at Monatomic (e.g. helium) |
| Amount of gas | A number, in mol | > 0 |
| Initial temperature | A number, in K | > 0 |
| Initial volume | A number, in m³ | > 0 |
| Final volume (optional) | A number, in m³ | > 0 |
| Final temperature (isochoric) (optional) | A number, in K | > 0 |
Formula and method
Formula
isothermal W = nRT ln(V₂/V₁); isobaric W = P(V₂ − V₁); isochoric W = 0; adiabatic T₂ = T₁(V₁/V₂)^(γ−1); ΔU = n C_v ΔT
IEEE-754 double precision; shown to the decimals indicated.
Ideal gas, C_v = 3R/2 (monatomic) or 5R/2 (diatomic), R = 8.314462618 J/(mol·K). W is work done by the gas.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Process = Isothermal; Gas = Monatomic (e.g. helium); Amount of gas = 1; Initial temperature = 300; Initial volume = 0.01; Final volume = 0.02.
| Result | Value |
|---|---|
| Work done by the gas | 1,728.944 J |
| Change in internal energy | 0 J |
| Heat added | 1,728.944 J |
| Final temperature | 300 K |
Example 2
Inputs: Process = Isobaric; Gas = Diatomic (e.g. air, N₂); Amount of gas = 2; Initial temperature = 300; Initial volume = 0.02; Final volume = 0.03.
| Result | Value |
|---|---|
| Work done by the gas | 2,494.339 J |
| Change in internal energy | 6,235.847 J |
| Heat added | 8,730.186 J |
| Final temperature | 450 K |
Example 3
Inputs: Process = Isochoric; Gas = Monatomic (e.g. helium); Amount of gas = 1.5; Initial temperature = 300; Initial volume = 0.01; Final volume = 0.01; Final temperature (isochoric) = 400.
| Result | Value |
|---|---|
| Work done by the gas | 0 J |
| Change in internal energy | 1,870.754 J |
| Heat added | 1,870.754 J |
| Final temperature | 400 K |
The first line is the headline result (work done by the gas). Below it the thermodynamic Processes Calculator lists change in internal energy, heat added and final temperature, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Isothermal example
W = 1 × 8.314 × 300 × ln 2 = 1,728.9 J. The temperature stays at 300 K, so ΔU = 0 and all the heat added becomes work: Q = W = 1,728.9 J (first law).
Ideal gas only
Real gases deviate from the ideal model at high pressure or low temperature. For monatomic gases γ = 5/3, diatomic 7/5. The first law ΔU = Q − W links the results.
How the result changes with amount of gas
Holding every other input at the first worked example, this table changes only amount of gas. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Amount of gas | Work done by the gas | Change in internal energy | Heat added |
|---|---|---|---|
| 0.5 | 864.472 J | 0 J | 864.472 J |
| 1 | 1,728.944 J | 0 J | 1,728.944 J |
| 2 | 3,457.888 J | 0 J | 3,457.888 J |
| 4 | 6,915.776 J | 0 J | 6,915.776 J |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Final volume: left empty shows "Enter the final volume." beside that field and no result.
- Final temperature (isochoric): left empty shows "Enter the final temperature." beside that field and no result.
Choosing between the Thermodynamic Processes Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Specific Heat Calculator](/science/specific-heat-calculator/) | solve for, mass and temperature change | Specific heat |
| [EER Calculator](/science/energy-efficiency-ratio-calculator/) | cooling capacity and power input | EER |
| [Heat Pump COP Calculator](/science/heat-pump-cop-calculator/) | use | COP |
| [Heat Transfer Calculator](/science/heat-transfer-calculator/) | thermal conductivity, area and temperature difference | Heat flow |
| [Thermal Expansion Calculator](/science/thermal-expansion-calculator/) | coefficient of linear expansion, original length and temperature change | Change in length |
Background: heat and temperature
The basic heat relation is Q = m × c × ΔT: heat in joules equals mass times specific heat capacity times temperature change. A positive Q means heat absorbed and a negative Q heat released, and a change in °C is numerically the same as a change in K.
It covers a change in temperature only. During melting or boiling the temperature stays constant while heat still flows (latent heat), which needs a separate term.
Assumptions and limitations
- Real gases deviate from the ideal model
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for final volume and final temperature (isochoric) to confirm this.
Frequently asked questions
What is an adiabatic process?
An adiabatic process exchanges no heat with its surroundings (Q = 0), so a gas that expands cools down.
What is γ?
The ratio of specific heats Cp/Cv.
Why is isochoric work zero?
The volume doesn't change.
What does the Thermodynamic Processes Calculator calculate?
Work, heat and internal energy for an ideal gas process. It returns Work done by the gas, Change in internal energy, Heat added and Final temperature.
What formula does the Thermodynamic Processes Calculator use?
isothermal W = nRT ln(V₂/V₁); isobaric W = P(V₂ − V₁); isochoric W = 0; adiabatic T₂ = T₁(V₁/V₂)^(γ−1); ΔU = n C_v ΔT. Ideal gas, C_v = 3R/2 (monatomic) or 5R/2 (diatomic), R = 8.314462618 J/(mol·K).
What do I need to enter in the thermodynamic Processes Calculator?
You enter Process, Gas, Amount of gas (mol), Initial temperature (K) and Initial volume (m³). Optional: Final volume (m³) and Final temperature (isochoric) (K).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Real gases deviate from the ideal model.
What does the “Process” option change?
It sets how the thermodynamic Processes is worked out. The choices are Isothermal, Isobaric, Isochoric and Adiabatic.
What is an example of a thermodynamic Processes result?
With process Isothermal, gas Monatomic (e.g. helium), amount of gas 1, initial temperature 300 and initial volume 0.01, the work done by the gas is 1,728.944 J.
Where does the method come from?
The method follows: CODATA 2018 gas constant; standard ideal-gas thermodynamics.
Related calculators
- Specific Heat Calculator — Specific heat capacity or heat required from Q = m c ΔT.
- EER Calculator — Energy efficiency ratio of an air conditioner and its COP equivalent.
- Heat Pump COP Calculator — Coefficient of performance from heat output and power input, or the Carnot limit.
- Heat Transfer Calculator — Conductive heat flow through a flat wall.
- Thermal Expansion Calculator — Change in length from a temperature change.
- Dew Point Calculator — Dew point from temperature and relative humidity.
Sources
- CODATA 2018 gas constant; standard ideal-gas thermodynamics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.