Activity: Intro to thermodynamics

Aims

  • Introduce the energy changes associated with gas transformations.
  • State the first law of thermodynamics.
  • Use the first law to predict energy changes for different gas transformations.
  • Define the terms, isochoric, isobaric, isothermal and adiabatic.
  • Sketch PV graphs for gas transformations.

Thermodynamic system

In this section we are going to look at the laws that model the energy flow in a thermodynamic system. The system considered will be a fixed mass of gas trapped in a cylinder by a piston but the laws apply to all thermodynamic systems.

Internal energy (U)

An ideal gas is made of a large number of perfectly elastic spheres moving in random motion. There are no forces between the particles unless they collide.

  • If you were to change the position of a gas atom would it require work to be done?
  • Why don't we consider the PE of gas atoms?

We already know that:

K E subscript a v end subscript equals 3 over 2 k T

A mole contains NA atoms

  • Write an expression for the internal energy of 1 mole of gas.

The universal gas constant, R = kNA

  • Write an expression for U in terms of R and show that for n moles

U equals 3 over 2 n R T

Heat transfer Q

When heat, Q is added to a fixed volume of gas it will increase the internal energy of the gas by ΔU. If energy is conserved:

Q equals capital delta U equals 3 over 2 n R capital delta T

  • Calculate the temperature rise when 2 J of heat are added to 1.203 x 10-3 moles of gas at constant volume.

Work done by a gas (W)

Let's consider a perfectly insulated cylinder of gas.

  • What does perfectly insulated imply about heat transfer between the gas and its surroundings?

The piston is pushed in.

  • Is work done?
  • Where does the energy transferred go?
  • What will happen to the pressure and temperature of the gas?

Consider 1.203x10-3moles of gas (you will have realised that this gives nR = 0.01JK-1 we can make the calculation even simpler if we use kPa as the unit for P and cm3 for V the equation become PV = 10T)

  • If the volume is 200 cm3 and pressure 100 kPa what is the temperature?
  • The volume is reduced to 100 cm3 causing the pressure to increase to 317 kPa. What is the temperature now?
  • Calculate the increase in internal energy.
  • How much work has been done on the gas?

Check you answer with this simulation, change the volume by dragging the blue dot.

Note that this process is reversible, you can compress the gas then let it expand and it returns to its original state.

The process is known as an adiabatic process.

Constant Pressure compression

Consider a gas where the piston has a constant force acting on it.

If heat is taken away what will happen to :

  • the temperature?
  • the pressure?
  • the position of the piston?
  • the volume?

As the volume gets less the density of gas will increase, this has the effect of increasing the pressure until it is the same as before. If this is done slowly we can say the pressure is constant.

Work done

in this example the pressure is constant which means the force, F on the piston is also constant. This means that work done is simply F x distance moved by the piston = FΔx

But P = F/A so F = PA where A is the area of the piston

This means that work done on the gas = PAΔx which is the same as PΔV where ΔV is the change in volume.
Note: PΔV is the area under the line on the PV graph.

Simulation

Ty removing energy from the gas in the simulation below and observe the effect on internal energy and volume.

Answer the following questions and then check you got them right using the simulation.

1.203 x 10-3 moles of a gas has volume 300 cm3, Pressure 200 kPa and temperature 6000K. It is cooled down at constant pressure until the volume equals 100 cm3. Calculate:

  • The final Temperature.
  • The work done on the gas
  • The reduction in internal energy.
  • The heat lost by the gas.

The first law of thermodynamics

Applying the law of conservation of energy to the gas we can see that the amount of heat added must equal the work done by the gas plus the increase in internal energy.

Q equals capital delta U plus W

We can apply this to the different gas transformations

Representing gas transformations on PV diagrams

The PV diagram is a very useful tool for helping to apply the second law. Remember that although there are only 2 axis (P and V) T is also represented by the set of isothermals that cover the space.
In this example (for 1.203 x 10-3 moles of course) we can see the isothermals for every 1000 K. They are not normally drawn but they are there.

Determine whether the temperature will increase or decrease in the following cases:

  • a gas expands from 100 cm3 to 300 cm3 at constant pressure
  • a gas changes from a pressure of 200 kPa and volume 50 cm3 to a pressure of 400 kPa and a volume of 100 cm3.

From the graph we can deduce

If temperature increases ⇨ Increase in internal energy (+ΔU)
If volume gets bigger ⇨ Work done by gas (+W)

We can now apply this to some specific examples

Constant Pressure changes (Isobaric)

Expansion (A → B)

Use the graph to determine

  • Is work done on the gas or by the gas?
  • Does temperature go up or down?

Use the first law to determine

  • is heat added or lost?

Compression (B → A)

Use the graph to determine

  • Is work done on the gas or by the gas?
  • Does temperature go up or down?

Use the first law to determine

  • is heat added or lost?

Constant Volume changes (Isochoric)

Heating (B → C)

Use the graph to determine

  • Is work done on the gas or by the gas?
  • Does temperature go up or down?

Use the first law to determine

  • is heat added or lost?

Cooling (C → B)

Use the graph to determine

  • Is work done on the gas or by the gas?
  • Does temperature go up or down?

Use the first law to determine

is heat added or lost?

Constant temperature (Isothermal)

Expansion (E → F)

Use the graph to determine

  • Is work done on the gas or by the gas?
  • Does temperature go up or down?

Use the first law to determine

  • is heat added or lost?

Compression (F → E)

Use the graph to determine

  • Is work done on the gas or by the gas?
  • Does temperature go up or down?

Use the first law to determine

is heat added or lost?

Adiabatic

This is a process where no heat is exchanged with the surroundings.

Expansion (G → H)

  • In this case no heat is exchanged so what can you say about the work done by the gas and the change in internal energy?

Compression (H → G)

  • What can you deduce about the work done on the gas and the change in internal energy?

To get a better understanding of the way the PV graph represents these changes you can build your own models in GeoGebra.
Thermodynamics simulation (GeoGebra)

First Law problems

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