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Wize University Chemistry Textbook > Thermodynamics: Part 1: (0th law, 1st law, Calorimetry, Enthalpy)

The 1st Law of Thermodynamics and Work

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Relating Work and the Ideal Gas LawNext Section
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The 1st Law of Thermodynamics

  • 1st Law of Thermodynamics: The energy of an isolated system is constant, ΔE=0\Delta E=0.
  • Sometimes this is re-worded as "energy cannot be created or destroyed".
  • EE is very difficult to measure so instead we measure changes in EEindirectly
  • The change in energy can be considered as a sum of heat and work done on and by the system. ΔE\Delta E is a state function, qqand ww are not.
ΔE=q+w\boxed{\Delta E=q+w}
ΔE is the change in Energy
q is heat (in J)
w is work (in J)

Wize Tip
Some profs write ΔE and others write ΔU. They mean the same thing! Both are referring to the internal energy of the system!

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From the 1st law of thermodynamics we can see that change in energy for system and surroundings must be equal in magnitude because the change in internal energy of the universe must be equal to zero.


ΔEuniv=ΔEsys+ΔEsurr=0\Delta E_{univ}=\Delta E_{sys}+\Delta E_{surr}=0
ΔEsurr=−ΔEsys\Delta E_{surr}=-\Delta E_{sys}
Examples:
  • If the system gains 5 J of energy, the surroundings (gains/loses)
    loses
    5 J of energy.
  • If the system loses 10 J of energy, the surroundings (gains/loses)
    gains
    10 J of energy.
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Internal Energy of Ideal Gases

The internal energy of an ideal gas is only dependent on temperature:
ΔE(T)\Delta E\left(T\right)
So for any Isothermal process involving an ideal gas,

ΔE =0\Delta E\ =0

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Signs of Heat and Work & Calculating Work

Recall the equation for the first law of thermodynamics:
ΔE=q+w\boxed{\Delta E=q+w}
ΔE is the change in Energy
q is heat (in J)
w is work (in J)


Photo by CNS Openstax / CC BY

In chemistry everything is with respect to the system so the following conventions exist:

Wize Concept
w > 0 if the surroundings do work on the system
w < 0 if the system does work on the surroundings
q > 0 if heat moves from the surroundings to the system
q < 0 if heat moves from the system to the surroundings

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When the external pressure is constant we can calculate work using the following equation:

w=−PexΔV\boxed{w=-P_{ex}\Delta V}
w=work (J)
Pext=constant external pressure (in kPa)
ΔV=Vf-Vi (in L)

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Example: Work Heat and Internal Energy of an Ideal Gas

20 L20\ L of an ideal gas isothermally expands to 40 L40\ L against a constant external pressure of 1 atm1\ atm. Calculate ww, qq, and ΔE\Delta E for this process.

We can use the following equation to calculate work first:
w=−pex(V2−V1)w=-p_{ex}(V_2-V_1)
Before plugging in values into this equation, check if the values we were provided have the correct units.
We need to convert the pressure from atm to kPa:
1atm x 101.3kPa1atm=101.3kPa1atm\ x\ \frac{101.3kPa}{1atm}=101.3kPa
Now we can plug in values into our equation to solve for work:

=(−101.3kPa)(40 L−20 L)=(-101.3kPa)(40\ L-20\ L)
w=−2026.5 J\boxed{w=-2026.5\ J}

The process is Isothermal expansion of an ideal gas so ΔE=0\boxed{\Delta E = 0}
ΔE=0=q+wq=−wq=2026.5 J\begin{array}{c} \Delta E=0=q+w\\[10pt] q=-w\\[10pt] \boxed{q=2026.5\ J} \end{array}

A system composed of 4.50 L of N2 in a cylinder expands against an external pressure of 300 kPa until its volume is 6.30 L.
  1. What is the value of w for this process?
  2. What would the value of w be if the external pressure was 0 kPa?
Fill in the following blanks!

How to fill in this table:
For the first column we have ∆U. Your options are temperature is constant, temperature increases, or temperature decreases
For the second column we have q. Your options are no heat is exchanged, heat enters the gas, or heat exits the gas
For the third column we have w. Your options are the volume is constant, the gas is compressed, or the gas expands.
∆U (Change in Internal Energy):q (heat):w (work):
Is positive when...
Is negative when...
Is 0 when...
Extra Practice
The enthalpy of combustion for ethanol (C2H5OH) is -1370.7 kJ/mol. Calculate q, w, ΔH and ΔU when 45g of ethanol are burned at 1atm and 298K.
Do not write the units when you input your answer.
Thermodynamics: Internal Energy
The enthalpy of combustion for ethanol (C2H5OH) is -1370.7 kJ/mol. Calculate q, w and ΔU when 45.0g of ethanol are burned at 1atm and 298K.
Answers need to be in scientific notation, with proper significant figures. Give all values in kJ.
A steam turbine uses some form of energy to evaporate water, heat the vapour and move a cylinder. We can think of this a constant pressure process, where H2O(l)→H2O(g)H_2O(l) → H_2O(g).
Complete the following sentences about this process by choosing one description per line. Enter the answers separated by a comma in the box below.
This process is exothermic / endothermic.
Thermodynamics: Pressure-Volume Work
Which of these reactions involve pressure-volume work being done on the system?
Thermodynamics: Pressure-Volume Work
A system composed of 4.50 L of N2 in a cylinder expands against an external pressure of 300 kPa until its volume is 6.30 L.
What is the value of w for this process?
What would the value be if the external pressure was 0 kPa?
Thermodynamics
2.3 moles of an ideal gas initially at -12oC and 16 atm underwent a complete expansion against a constant external pressure of 1atm and did 1.1kJ of work. Calculate ΔE, Δ𝐻, 𝑎𝑛𝑑 𝑞 for this process.
A Piston containing an 1.3 moles of an Ideal Gas undergoes a compression from 32 L to 27 L against a constant external pressure of 178 kPa. During this transformation the temperature does not change. Calculate ΔE,q and w\Delta E, q\ and\ wfor this transformation. Report your answers in Joules with no decimal points. You do not have to include the unit in your answer
If an exothermic process releases 555 J of heat to the surroundings when the volume of the system is kept constant, how would the amount of heat released change if the system were allowed to expand instead?
Thermodynamics: Work
The diagram below has 4 identical gas systems at a constant pressure. Assume that the long arrows are all the exact same length and have the exact same energy. Assume that all the short arrows have the exact same length and exact same energy.
q=heat, w=work. Which of the following statements is true?
The enthalpy of combustion for ethanol (C2H5OH) is -1338.9 kJ. Calculate q, w, ΔH and ΔU when ethanol is burned at 1atm and 298K.
Based on signs of q and w, was heat released or gained, work done on or by system?
Thermodynamics: Work
4 moles of neon was confined to a 8L flask initially at room temperature underwent an isothermal expansion into a vacuum at 348K and constant volume. Calculate ∆𝑈, w, 𝑎𝑛𝑑 𝑞 for this process.
The enthalpy of combustion for ethanol (C2H5OH) is -1370.7 kJ/mol. Calculate q, w, ΔH and ΔU when 45g of ethanol are burned at 1atm and 298K.
The enthalpy of combustion for ethanol C2H5OH is -1370.7 kJ/mol. Calculate q, w, ΔH and ΔU when 45 g of ethanol are burned at 1 atm and 298 K.
q
w
Thermodynamics: Review
Fill in the following blanks!
How to fill in this table:
For the first column we have ∆U. Your options are temperature is constant, temperature increases, or temperature decreases