6.3 First Law of Thermodynamics

6.3 First Law of Thermodynamics

Work and Heat

• Recall that:  W = Fd  

• Pressure is defined as force per area, so  F = PA  

• This means that  W = PAd , but  Ad = ΔV = V_f ​− V_i​   

• Finally, we say that  W = P (V_f​−V_i​)  

• This equation relates the work done by a gas to the pressure and the change in volume, but where does the heat come in?

Heat and Internal Energy

• Heat energy is measured in joules, and so is work.

• They both affect the internal energy, U , of a substance in a system. 

• Internal energy is the sum of the kinetic, potential, chemical, electrical, nuclear, and all other forms of energy associated with the atoms and molecules of the system.

• Let's illustrate all of this with an example.

Example

• Suppose we have a gas in a closed cylinder with a piston at one end.

• If we had an external heat source (Q), it would increase the gas molecules' kinetic energy  (ΔQ),  so the gas expands and pushes the piston through a distance, d.

• The change in internal energy of the system is equal to the heat flow into the system minus the work done by the system

• Mathematically:  ΔU = Q − W  

The First Law of Thermodynamics

• The equation that we just found in the example is the mathematical description of the First Law of Thermodynamics. (ΔU = Q − W ) 

• The first law is basically just a restatement of the conservation of energy for a specific thermodynamic process.

• Each of the quantities in the equation can be either positive or negative, but what does their sign mean?

Open Ended

What do you think that the sign of the various quantities in the First Law of Thermodynamics mean?

Review Signs of Quantities

• Let's look at what the signs of the quantities of the First Law of Thermodynamics mean about the system:

• Do these make sense?

Four Thermodynamic Processes

• Now that we have learned the First Law of Thermodynamics, we want to use it to look at four types of thermodynamic processes.

• While we discuss these processes, take note of the names and their meaning to help you understand what is happening.

• You can then relate this to the variable that is held constant.

Isothermal Process

• In an isothermal process, temperature remains constant throughout the system.

• This implies that the internal energy is also constant, so ΔU = 0   

• This means that  Q = W  

• During an isothermal process, the piston moves slowly while the system is held in thermal contact with a heat reservoir at a fixed temperature.

Graph of Isothermal Process

• For an isothermal process, PV = constant. 

• This actually is derived from the ideal gas law  PV = nRT  

• Each point on the curve represents a specific value of the pressure and volume (the state of the system).

Isobaric Process

• An isobaric process is one in which the pressure remains constant throughout the system.

• The volume is allowed to change (expand or contract), and therefore the temperature will also change.

• As the internal energy changes, work is done by the system (expansion) or work is done on the system (compression).

• Therefore, none of the quantities in the first law of thermodynamics ever reduces to zero.

Graph of Isobaric Process

• If a system undergoes expansion, then it does work on its surroundings.

• This is represented by a horizontal line on a PV diagram.

• If the system undergoes compression (where the surroundings do work on the system) that's also represented by a horizontal line on the PV diagram.

• The only difference is that  V_i > V_f​ 

Isovolumetric Process

• An isovolumetric (sometimes called isometric or isochoric) process is one in which the volume remains constant throughout the system

• Since the volume is constant, W = 0   

• This means that  ΔU = Q  

• When heat is added to the system, the internal energy increases, and the pressure on the walls increases.

• If heat is removed from the system, internal energy decreases and the pressure on the walls decreases.

Graph of Isovolumetric Process

• In an isovolumetric process, the volume is kept constant and the pressure is allowed to vary.

• This leads to a vertical line on the PV graph.

• Since there is no change in volume, no work is done.

• The graph of an isovolumetric process can easily be confused with the graph of an isobaric process.

Adiabatic Process

• In an adiabatic process, no heat transfers into or out of the system.

• A system that expands under adiabatic conditions does positive work so the internal energy decreases along with the temperature.

• A system that contracts under adiabatic conditions does negative work so the internal energy increases along with the temperature.

• Mathematically:  ΔU = −W  

Graph of Adiabatic Process

• During an adiabatic process, no heat is allowed into or out of the system.

• This process follows a curve where PV = constant.

• In an adiabatic process, the pressure drops off more than in an isothermal process that occurs between the same two volumes.

• The adiabatic path is steeper because the gas loses internal energy as it does work.

Multiple Choice

40J of work is done by a gas when the system has an increase in internal energy of 125J. What energy is needed to do so?

• 85J
• 205J

• Can't accomplish

• 165J

Multiple Choice

1200 J of heat are added to a sample of gas while 400 J of work is done by the gas. What is the change in internal energy of the gas?

• 1600 J
• -1600 J

• -800 J

• 800 J

Multiple Choice

What does the "U" stand for the formula  ΔU = Q − W ?

• Internal energy
• Heat
• Work
• Temperature

Multiple Choice

Calculate the heat transfer to the environment if the system produces a work of 45 kJ and receives 9 kJ in the way of heat. The enthalpy (internal energy) difference of the system is equal to 55 kJ.

• 19 kJ

• 91 kJ

• 10 kJ
• 1 kJ

Multiple Choice

The product of the pressure and volume of a system has the same SI units as which one of the following choices?

• Distance (m)

• Temperature (C)

• Work (J)

• Time (s)

Multiple Choice

When applying the first law of thermodynamics to a system, when is heat a positive quantity?

• When work is done on the system

• When the system

• When it is added to the system
• When it is removed from the system

Multiple Choice

What is the name of the process in which pressure remains constant.

• isothermal process
• isobaric process
• adiabatic process
• isochoric process

Multiple Choice

For an isothermal process, which of the following statements is correct?

• Work and heat balance each other, so that there is no change in internal energy.

• Work, heat, and internal energy all undergo changes.

• No work is done; internal energy change is due to heat.

• No energy is transferred as heat; internal energy change is due to work.

Multiple Select

Which of these processes have a straight line when plotted on a PV graph?

• Isochoric process
• Isobaric process
• Adiabatic process
• Isothermal process

Multiple Choice

The PV diagram for an adiabatic process looks similar to the PV diagram for...

• isobaric process
• isovolumetric process

• adiabatic process

• isothermal process

Multiple Choice

In an adiabatic process, what equals zero?

• T

• Q

• W

• ΔU