Thermodynamic Processes
Analyze isochoric, isobaric, isothermal, and adiabatic processes of ideal gases. Get final p, V, T, ΔU, W, and Q with interactive charts for physics students.
About This Calculator
The Thermodynamic Processes Calculator helps students, engineers, and physicists analyze the four fundamental ideal gas processes: isochoric (constant volume), isobaric (constant pressure), isothermal (constant temperature), and adiabatic (no heat transfer). Enter the initial state of the gas (pressure, volume, temperature, and amount) along with one known final parameter, and the calculator determines all final state variables plus the change in internal energy, work done by the gas, and heat transferred.
All calculations are based on the ideal gas law pV = nRT and the combined gas law p₁V₁/T₁ = p₂V₂/T₂, combined with the first law of thermodynamics ΔU = Q - W. The calculator supports three gas types with correct theoretical molar heat capacities: monatomic (Cv = 3R/2, γ = 5/3), diatomic (Cv = 5R/2, γ = 7/5), and polyatomic (Cv = 3R, γ = 4/3). For each process type, the appropriate formula automatically selects the relationship between p, V, and T. Isochoric processes follow p/T = constant with zero work; isobaric processes follow V/T = constant with work W = pΔV; isothermal processes follow pV = constant with ΔU = 0 and W = Q = nRT·ln(V₂/V₁); adiabatic processes follow pV^γ = constant with Q = 0 and ΔU = -W.
Regional Notes
India (IN) & International (SI): This calculator exclusively uses SI units — pressure in kilopascals (kPa), volume in cubic meters (m³), temperature in kelvin (K), amount in moles (mol), and energy in joules (J). 1 atm = 101.325 kPa. Standard temperature is 273.15 K (0 °C). For engineering applications, 1 bar = 100 kPa.
United States (US): While US engineering often uses psi and °F, this calculator standardizes on SI for scientific accuracy. 1 psi = 6.89476 kPa. To convert °F to K: K = (°F + 459.67) × 5/9. The R value of 8.314 J/(mol·K) is equivalent to 1.987 cal/(mol·K) or 0.08206 L·atm/(mol·K).
United Kingdom (UK): UK A-level and university physics courses use SI units (kPa, m³, K, J) as implemented here. British engineering commonly uses bar (1 bar = 100 kPa) for pressure. The gas constant R = 8.314 J/(mol·K) is standard across all UK and European curricula for thermodynamics calculations.
Frequently Asked Questions
What are the four thermodynamic processes of ideal gases?
The four fundamental thermodynamic processes for ideal gases are isochoric (constant volume), isobaric (constant pressure), isothermal (constant temperature), and adiabatic (no heat transfer). In an isochoric process, pressure is proportional to temperature (p/T = constant). In an isobaric process, volume is proportional to temperature (V/T = constant). In an isothermal process, pressure is inversely proportional to volume (pV = constant). In an adiabatic process, pV^γ = constant where γ is the heat capacity ratio (Cp/Cv).
How do you calculate work done in each thermodynamic process?
Work done by the gas depends on the process type. For isochoric processes, no work is done (W = 0) because volume is constant. For isobaric processes, W = p·ΔV where p is constant pressure and ΔV is volume change. For isothermal processes, W = nRT·ln(V2/V1). For adiabatic processes, W = (p2V2 - p1V1)/(1 - γ) where γ is the heat capacity ratio. Work is positive when the gas expands and negative when compressed.
What is the first law of thermodynamics and how is it applied?
The first law of thermodynamics states that the change in internal energy of a system equals the heat added to the system minus the work done by the system: ΔU = Q - W. For isochoric processes, Q = ΔU since W = 0. For isothermal processes, ΔU = 0 so Q = W. For adiabatic processes, Q = 0 so ΔU = -W. For isobaric processes, Q = ΔU + W = nCpΔT. The internal energy change always equals nCvΔT regardless of the process path.
What are the values of Cv and Cp for different gases?
For ideal gases, molar heat capacities depend on molecular structure. Monatomic gases (He, Ne, Ar) have Cv = 3R/2 ≈ 12.47 J/(mol·K) and Cp = 5R/2 ≈ 20.79 J/(mol·K) with γ = 5/3 ≈ 1.667. Diatomic gases (N2, O2, air) have Cv = 5R/2 ≈ 20.79 J/(mol·K) and Cp = 7R/2 ≈ 29.10 J/(mol·K) with γ = 7/5 = 1.4. Polyatomic gases (CO2, CH4) have Cv = 3R ≈ 24.94 J/(mol·K) and Cp = 4R ≈ 33.26 J/(mol·K) with γ = 4/3 ≈ 1.333.
What is the combined gas law formula?
The combined gas law combines Boyle's law, Charles's law, and Gay-Lussac's law into a single formula: pV/T = k, where k is constant for a fixed amount of gas. For calculations involving state changes of a fixed amount of gas, the formula becomes p1V1/T1 = p2V2/T2. This law forms the basis for solving isochoric (V constant), isobaric (p constant), and isothermal (T constant) processes by removing the constant parameter from the equation.
How does an adiabatic process differ from isothermal?
In an isothermal process, temperature remains constant because the system exchanges heat with the surroundings (Q ≠ 0) to maintain temperature, while in an adiabatic process, no heat is exchanged (Q = 0) so temperature changes. Isothermal processes are slow, allowing heat to flow, while adiabatic processes are rapid with no time for heat transfer. In an adiabatic expansion, the gas cools (T decreases), and in an adiabatic compression, the gas heats up (T increases), following T·V^(γ-1) = constant.
What is the ideal gas law and what is R?
The ideal gas law is pV = nRT, where p is pressure, V is volume, n is the number of moles of gas, T is absolute temperature in kelvin, and R is the universal gas constant. The value of R is 8.314462618 J/(mol·K) in SI units. Other common values are 0.082057 L·atm/(mol·K), 62.3637 L·mmHg/(mol·K), and 1.987 cal/(mol·K). This calculator uses R = 8.314 J/(mol·K) with p in kPa, V in m³, T in K, and n in mol.
Can I use this calculator for real gases?
This calculator assumes ideal gas behavior, which is accurate for most gases at low to moderate pressures and high temperatures relative to their critical point. For real gases under extreme conditions (very high pressure, near liquefaction), deviations from ideal behavior occur and the van der Waals equation or other real gas models should be used. The calculator supports monatomic (He, Ne, Ar), diatomic (N2, O2, air), and polyatomic (CO2, CH4) ideal gases with correct theoretical heat capacities.