Physics 2nd Paper · Classes 11-12 · Chapter 1 · 1.3

Thermal System and Isothermal Change.

Squeeze a bicycle pump hard and the barrel warms up; squeeze it slowly and you hardly notice. Same gas, same compression, yet the temperature behaves differently. This note shows when a gas holds its temperature steady, and what rule then ties its pressure to its volume.

1. The thermal system and its three kinds

The definite thermal part of the material world that we choose to look at in an experiment is a thermal system. The gas inside a cylinder with a piston is a thermal system, and everything around it is the surroundings. Every system has a definite volume, mass and internal energy.

What passes between the system and its surroundings sorts systems into three kinds. An open system exchanges both mass and energy. A closed system exchanges only energy, not mass. An isolated system is not affected by its surroundings at all: it exchanges neither mass nor energy. Open and closed both let energy through, so it is easy to mix them up; the difference is mass. Answer the two questions in the tree below.

2. Four kinds of change, and the isothermal one

Thermodynamic changes in a thermal system come in four kinds: isothermal, adiabatic, constant-volume (isochoric) and constant-pressure (isobaric). The book misprints the constant-volume one as isochronic; the right word is isochoric. This note is about the isothermal change, and the adiabatic one comes in the next.

A change in which the pressure and volume of a gas change but the temperature stays constant is an isothermal change, and the way it takes place is an isothermal process.

How can the temperature stay fixed? Compress a gas suddenly and heat is produced, so its temperature rises; expand it suddenly and it loses heat, so its temperature falls. But do it slowly, supplying or removing heat as needed, and the temperature holds. That is the pump story from the start.

Then pressure and volume obey Boyle's law: P ∝ 1/V, that is, PV = constant. The graph of P against V is a rectangular hyperbola. Each temperature gives its own curve, and these are called isotherms. Drag the handle: both quantities change, yet the product does not move.

3. Conditions for an isothermal change

There are four conditions for an isothermal change: the gas sits in a good conductor of heat; the medium around the container has a high heat capacity; the pressure changes slowly; and heat taken in or given out keeps the temperature fixed. The adiabatic change needs exactly the opposite. Share six conditions between the two changes below.

The isothermal change is a slow process, and its graph is less steep than the adiabatic graph.

When a gas expands, the work done in the isothermal process is greater than in the constant-pressure process. In the isothermal case the internal energy does not change, du = 0, so all the heat supplied becomes work: dQ = dW. At constant pressure part of the heat goes into raising the internal energy, and less is left for work.

4. Two calculations

Example 1. A gas of 10 L at 300 K and 4 atm has its pressure doubled isothermally. The temperature is fixed, so Boyle's law gives P1V1 = P2V2, and V2 = P1V1/P2 = 4 × 10/8 = 5 L. Double the pressure, half the volume.

Example 2. 3 mol of a diatomic gas at T1 = 30°C expands isothermally from V to 2V. The work in an isothermal expansion is W = nRT1 ln(V2/V1). With T1 = 30 + 273 = 303 K, W = 3 × 8.31 × 303 × ln 2 = 5236 J. The formula takes the ratio of the volumes, not their difference.

Of the four changes, the constant-volume one turns up in exams through a familiar sight.

5. Check yourself

Three questions in the exam's style. Start with the first.

Now the second.

And the last.

The whole note on eight cards.

Source: Physics 2nd Paper, Classes 11-12 (NCTB), Chapter 1 “Thermodynamics”, section 1.3.