The first law of thermodynamics IB DP Physics Study Notes - 2025 Syllabus

The first law of thermodynamics IB DP Physics Study Notes

The first law of thermodynamics IB DP Physics Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

The first law of thermodynamics, as given by $ Q = \Delta U + W $, results from the application of conservation of energy to a closed system and relates the internal energy of a system to the transfer of energy as heat and as work.
The work done by or on a closed system, as given by $ W = P\Delta V $, when its boundaries are changed, can be described in terms of pressure and changes in the volume of the system.

Standard level and higher level: There is no Standard level content
Additional higher level: 8 hours

IB DP Physics 2025 -Study Notes -All Topics

The Laws of Thermodynamics

A note on language:

Heat is NOT Internal Energy

Heat is the flow of thermal energy from one object to another and will increase the internal energy of the receiver and decrease the internal energy of the donor.

HEAT🡪 more random motion (<KE>)🡪 higher temperature
HEAT🡪 stretched bonds 🡪 higher PE, without changing T

This is similar to saying work is not mechanical energy.
Work is the transfer of mechanical energy from one object to another.

The 1st Law of Thermodynamics

Energy is conserved – it is neither created nor destroyed.
Internal energy of a system may change as any combination of:
- (i) Doing work on the system
- (ii) Transferring energy to or from the system as a result of a difference in temperature

When $Q > 0$, energy is transferred from the surroundings to the system because $T_{surroundings} > T_{system}$.

If $\Delta U > 0$, there has been an increase in internal energy.

If $W > 0$, work is done *by* the system on the environment as it expands.

Using the 1st Law of Thermodynamics

A system can change its state. A state is a unique set of values for P, V, n, & T. This is why PV = nRT is also called a “State Equation”

There are 4 basic processes with n constant:

Isobaric, a change at constant pressure
Isochoric or isovolumetric, a change at constant volume, W = 0
Isothermal, a change at constant temperature (ΔU = 0)
Adiabatic, a change at no heat (Q = 0)

Work done in an isobaric change

Isobaric = constant pressure
As the gas expands, the piston moves up by a distance $d$.
As a result, volume increases $\Delta V = Ad$
The force of the gas on piston $F = PA$
The work done by the gas on the surroundings:
$W = Fd = PAd = P\Delta V$

Constant pressure process – isobaric process

In an isobaric process, p does not change.
As an example of an isobaric experiment, suppose we take a beaker that is filled with an ideal gas, and stopper it with a gas-tight, frictionless cork and a weight, as shown.
The weight F causes a pressure in the gas having a value given by p = F / A, where A is the area of the cork in contact with the gas.
If we now heat up the gas it will expand against the cork, pushing it upward:
Since neither F nor A change, p remains constant.

Here is the text from the image, using LaTeX for the formulas and simple typing for the rest:

Constant pressure process – work done by a gas

From the previous slide: $p = \frac{F}{A} \rightarrow F = pA$.
From the picture note that $\Delta V = Ax$.
Recall the work $W$ done by the gas is just the force $F$ it exerts on the weighted cork times the displacement $x$ it moves the cork. Thus
$W = Fx = pAx = p\Delta V$.

FYI

• If $\Delta V > 0$ (gas expands) then $W > 0$.

• If $\Delta V < 0$ (gas contracts) then $W < 0$.

EXAMPLE

Show that for an isolated ideal gas $ V \propto T $ during an isobaric process.

▶️Answer/Explanation

SOLUTION:

Start with the ideal gas law:
\[
pV = nRT
\]

Rearranging for $ V $:
\[
V = \frac{nR}{p}T
\]

An isolated system means $ n $ is constant (no gas is added to or lost from the system).
An isobaric process means $ p $ is constant.

Since $ n $, $ p $, and $ R $ are constants:
\[
V = \frac{nR}{p}T = (\text{CONST})T
\]

Thus,
\[
V \propto T \quad \text{(isobaric process)}.
\]

FYI: This relationship is known as Charles’ Law.

The first law of thermodynamics IB DP Physics Study Notes

The first law of thermodynamics IB DP Physics Study Notes - 2025 Syllabus