Thermodynamic Processes Calculator
Calculate work for isothermal, isobaric, isochoric, and adiabatic ideal gas processes with step-by-step formulas.
Ideal Gas Thermodynamic Processes
Thermodynamic processes describe how an ideal gas moves between states while exchanging work and heat. Each named process holds one variable fixed: temperature (isothermal), pressure (isobaric), volume (isochoric), or heat flow (adiabatic). The work integral depends on which variable stays constant.
Work Formulas
Boundary work for common ideal-gas processes:
$$W_{\text{isothermal}} = nRT \ln\!\left(\frac{V_2}{V_1}\right)$$ $$W_{\text{isobaric}} = P\,\Delta V$$ $$W_{\text{isochoric}} = 0$$ $$W_{\text{adiabatic}} = \frac{P_2 V_2 - P_1 V_1}{\gamma - 1}$$\(n\) is amount of substance, \(R = 8.314\,\text{J/(mol·K)}\), and \(\gamma = C_p/C_v\). Positive work means the gas expands against its surroundings; negative work means the surroundings compress the gas.
Choosing a Process
Slow contact with a large heat bath approximates isothermal behavior. Open piston expansion against constant atmospheric pressure is often modeled as isobaric. Rigid tank heating is isochoric. Fast compression with insulated walls is closer to adiabatic.
Related tools: Ideal Gas Law Calculator and Specific Heat Calculator.
Frequently Asked Questions
Why is isochoric work zero?
Work requires a volume change. In a rigid container the boundary does not move, so \(W = \int P\,dV = 0\).
What is γ for air?
Dry air at room temperature is often taken as γ ≈ 1.4. Use the value that matches your gas and temperature range.
Can work be negative?
Yes. Compression work done on the gas is negative when using the "work done by the gas" sign convention.
Do I need moles for every process?
Only isothermal work uses \(nRT\). Isobaric work needs pressure and volume change. Adiabatic work uses pressures and volumes at both states.
Is this the same as enthalpy change?
For isobaric processes, \(Q = \Delta H\) when only boundary work matters. This tool reports mechanical work, not total energy balance.
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