Thermodynamic Processes: Isothermal, Adiabatic and More

A thermodynamic process is a change in which a system goes from one equilibrium state to another, for example a gas expanding in a cylinder. Four basic ideal processes are isothermal, adiabatic, isobaric, and isochoric, each keeping one quantity constant.

These processes are building blocks of engine cycles. Real machines are not perfectly isothermal or adiabatic, but approximating steps this way lets us calculate heat, work, and efficiency clearly.

Key Concepts

Isothermal means constant temperature, delta T = 0. Isobaric means constant pressure. Isochoric or isovolumetric means constant volume, so boundary work is zero. Adiabatic means no heat exchange, Q = 0, usually by insulation or very fast change. For an ideal gas PV = nRT links pressure in pascal, volume in cubic metre, amount n in mole, gas constant R = 8.314 joule per mole per kelvin, T in kelvin. Internal energy of ideal gas depends only on temperature.

Formulas

Isothermal ideal gas: delta U = 0, Q = W_by = nRT ln(V2/V1). Adiabatic: Q = 0, delta U = -W_by, and PV^gamma = constant where gamma = Cp/Cv. Isobaric: W_by = P(V2 - V1), Q = nCp delta T. Isochoric: W_by = 0, Q = delta U = nCv delta T. These assume reversible ideal-gas behaviour.

Worked Example

One mole of ideal gas at 300 kelvin expands isothermally from 0.010 to 0.020 cubic metre. Find work done.

Step 1: W = nRT ln(V2/V1). Step 2: nRT = 1 x 8.314 x 300 = 2494 joule. Step 3: ln(0.020/0.010) = ln 2 = 0.693. Step 4: W = 2494 x 0.693 = 1728 joule. Since delta U = 0, heat absorbed Q = 1728 joule. The gas must be in contact with a reservoir to stay at 300 kelvin while expanding.

Common Misconceptions

• Adiabatic means constant temperature: Wrong. Adiabatic means no heat flow; temperature usually changes during expansion or compression.
• Isothermal gas needs no heat: Wrong. Expanding isothermal gas absorbs heat equal to work done.
• Isochoric process can do boundary work: Wrong. If volume does not change, P dV work is zero.

Real-World Applications

Diesel compression is nearly adiabatic, heating air enough to ignite fuel. Slow expansion in a thermostatted lab cylinder approximates isothermal. Boiling water at atmospheric pressure is nearly isobaric. A sealed rigid pressure cooker heating at fixed volume is isochoric until the valve releases steam. Carnot and Otto cycles combine these ideal steps.

Isothermal keeps T constant, adiabatic keeps Q zero, isobaric keeps P constant, and isochoric keeps V constant. Knowing which quantity is fixed tells you immediately which formula for heat, work, and internal energy to use.