Worksheet: Energy Changes in Gas Expansions

In this worksheet, we will practice classifying gas expansion and compression processes based on changes in heat, entropy, enthalpy, or internal energy.

Q1:

Consider 0.1 mol of an ideal gas contained in a cylinder of volume 2.5 dm3 at a pressure of 1 bar and a temperature of 301 K. Next, suppose you consider three different processes for changing the state of the gas sample to one in which the volume is reduced to 0.25 dm3, the pressure is increased to 10 bar, and the temperature is 301 K (the same as the temperature in the initial state). The paths of the three alternative processes are specified as follows.

Process 1 is a two-step process in which the gas sample is first heated at constant volume until the pressure reaches a value of 10 bar, and then the gas is cooled under constant pressure (10 bar) until its equilibrium volume is reduced to 0.25 dm3 and its temperature is 301 K.

Process 2 is a two-step process in which the gas sample is first cooled under constant pressure (1 bar) until its equilibrium volume is reduced to 0.25 dm3, and then the gas is heated under constant volume conditions until its pressure reaches a value of 10 bar and its temperature is 301 K.

Process 3 is a single-step process in which the gas is isothermally compressed from its initial state to its final state at a fixed temperature of 301 K.

Which of the three processes above would require the least amount of work in effecting the specified change of state, and what would be the Ξ”π‘ˆ (change in internal energy) for this process?

  • AProcess 2, Ξ”π‘ˆ=0
  • BProcess 1, Ξ”π‘ˆ=0
  • CProcess 3, Ξ”π‘ˆ=0
  • DProcess 2, Ξ”π‘ˆ>0

Q2:

Consider a process in which a gas is expanded adiabatically and reversibly under constant-pressure conditions, and the amount of work done by the gas in this process is 10 kJ. What changes in the internal energy (π‘ˆ) and entropy (𝑆) of the gas will accompany this process?

  • AThere is not enough information to determine the values of Ξ”π‘ˆ, Δ𝑆.
  • B Ξ” π‘ˆ = βˆ’ 1 0 k J , Ξ” 𝑆 = 0
  • C Ξ” π‘ˆ = 0 , Ξ” 𝑆 = 1 0 / J K
  • D Ξ” π‘ˆ = 1 0 k J , Ξ” 𝑆 = 0

Q3:

Consider a process in which a 2 mol sample of a certain gas is heated reversibly from 275 K to 375 K under a constant pressure of 1 bar, and the entropy change for the gas is Δ𝑆=13.3/JK. What will the value of Δ𝑆 for a process in which the same gas sample is heated irreversibly from 275 K to 375 K under a fixed pressure of 1 bar?

  • A Ξ” 𝑆 > 1 3 . 3 / J K
  • BThere is not enough information provided to answer this question.
  • C Ξ” 𝑆 = 1 3 . 3 / J K
  • D Ξ” 𝑆 < 1 3 . 3 / J K

Q4:

Which of the following processes carried out on a 1 mole sample of a monatomic gas (assumed to exhibit ideal gas 𝑃𝑉𝑇 behavior) will result in the greatest increase in the entropy of the gas?

  • AHeating the gas from 300 K to 600 K under constant volume conditions
  • BIsothermal expansion from a volume of 5 L to a volume of 10 L
  • CReversible adiabatic expansion from a volume of 5 L to a volume of 10 L
  • DIsothermal expansion from a volume of 10 L to a volume of 15 L

Q5:

Which of the following statements is false?

  • AThe Joule–Thomson effect relates to the temperature change occurring in a gas during an isenthalpic expansion of the gas.
  • BCalorimetry involves the measurement of heat transfer during a physical or chemical process.
  • CFor any given change of state, the work done by a system in an irreversible process is always greater than that in a reversible process.
  • DAccording to the third law of thermodynamics, the entropies of all perfectly crystalline substances must be the same at the absolute zero of temperature (i.e., at 𝑇=0K).

Q6:

Consider a container with rigid, adiabatic walls that is fitted with a partition that separates the container into two chambers (one having twice the volume of the other). The larger chamber contains a 2 mol sample of N()2g at 298 K and 1 bar pressure, and the smaller chamber contains a 1 mol sample of He()g at 298 K and 1 bar pressure. The partition between the chambers is removed and the N2 and He gases are allowed to mix. This mixing process is isothermal and also adiabatic. Assuming that the gases behave ideally, what would the Ξ”π‘ˆ (change in internal energy), Δ𝐻 (enthalpy change), and Δ𝑆 (entropy change) that accompany this mixing process be?

  • A Ξ” π‘ˆ = 0 , Ξ” 𝑆 = 1 5 . 8 8 / J K , there is not enough information to determine Δ𝐻.
  • B Ξ” π‘ˆ = 0 , Ξ” 𝐻 = 0 , Ξ” 𝑆 = 1 5 . 8 8 / J K
  • C Ξ” π‘ˆ = Ξ” 𝐻 = Ξ” 𝑆 = 0
  • D Ξ” π‘ˆ = 0 , Ξ” 𝐻 = 0 , Ξ” 𝑆 = βˆ’ 1 5 . 8 8 / J K

Q7:

Suppose a 1 mol sample of an ideal gas is expanded isothermally and reversibly from a volume of 10 L to a volume of 20 L at a temperature of 298 K. How much work (𝑀) is done in this process, and what are the changes in the internal energy (Ξ”π‘ˆ) and entropy (Δ𝑆) of the gas?

  • A 𝑀 = 0 , Ξ” π‘ˆ = 1 , 7 1 7 J , Ξ” 𝑆 = 5 . 7 6 / J K
  • B 𝑀 = βˆ’ 1 , 7 1 7 k J , Ξ” π‘ˆ = 0 , Ξ” 𝑆 = 5 . 7 6 / J K
  • C 𝑀 = 1 . 7 1 7 k J , Ξ” π‘ˆ = 0 , Ξ” 𝑆 = 5 . 7 6 / J K
  • D 𝑀 = βˆ’ 1 . 7 1 7 k J , Ξ” π‘ˆ = βˆ’ 1 , 7 1 7 k J , Ξ” 𝑆 = 0

Q8:

Suppose you want to cool a sample of N()2g from 25∘C to βˆ’195∘C by a one-step process involving a Joule–Thomson expansion in which the final pressure is 1 bar. The Joule–Thomson coefficient for N()2g over the specified temperature range may be taken to be πœ‡=0.75/ο…οŠ±οŒ³Kbar. Determine if the enthalpy change (Δ𝐻) for this cooling process is less than, greater than, or equal to zero and calculate to the nearest bar what the initial pressure (𝑃)initial of the gas must be in order to produce the desired temperature change.

  • A 𝑃 = 2 9 2 i n i t i a l b a r , Ξ” 𝐻 > 0
  • B 𝑃 = 2 9 2 i n i t i a l b a r , Ξ” 𝐻 < 0
  • C 𝑃 = 2 2 5 i n i t i a l b a r , Ξ” 𝐻 = 0
  • D 𝑃 = 2 9 2 i n i t i a l b a r , Ξ” 𝐻 = 0
  • E 𝑃 = 2 2 5 i n i t i a l b a r , Ξ” 𝐻 > 0

Q9:

Methanol boils at a temperature of 337.2 K under standard pressure (𝑃=1)bar conditions, and its standard enthalpy of vaporization is Δ𝐻=35.27/⦡vapkJmol. What is the standard entropy of vaporization of methanol?

  • A104.6 J/Kβ‹…mol
  • B βˆ’ 1 0 4 . 6 J/Kβ‹…mol
  • CThere is not enough information provided to answer this question.
  • D βˆ’ 1 0 4 . 6 Γ— 1 0   J/Kβ‹…mol
  • E104.6 kJ/Kβ‹…mol

Q10:

What is the standard molar entropy 𝑆⦡ of oxygen atoms at 298 K (assumed to behave as an ideal gas)?

Q11:

The enthalpy of vaporization of methanol is 35.27 kJ/mol at its normal boiling point of 64.1∘C. What is the entropy of vaporization of methanol (Δ𝑆)⦡vap at this temperature, and what is the entropy change in the surroundings (Δ𝑆)surroundings when a mole of methanol is vaporized at a temperature of 64.1∘C and a pressure of 1 bar?

  • A Ξ” 𝑆 = βˆ’ 1 0 4 . 6 / β‹… ⦡ v a p J K m o l for methanol, Δ𝑆=104.6/β‹…surroundingsJKmol
  • B Ξ” 𝑆 = 1 0 4 . 6 / β‹… ⦡ v a p J K m o l for methanol, Δ𝑆=βˆ’104.6/β‹…surroundingsJKmol
  • C Ξ” 𝑆 = 5 5 0 . 2 / β‹… ⦡ v a p J K m o l for methanol, Δ𝑆=0surroundings
  • D Ξ” 𝑆 = 1 0 4 . 6 / β‹… ⦡ v a p J K m o l for methanol, Δ𝑆=0surroundings

Q12:

In a free (Joule) expansion of a gas, no work is done either on or by the gas. If the gas in such a process behaves as an ideal gas, which of the following statements is also true for the free-expansion process?

Note that π‘ˆ is the internal energy of the gas, 𝑆 is the entropy of the gas, π‘ž is the heat exchanged between the gas and its surroundings, 𝑉initial is the initial volume of the gas before expansion, and 𝑉final is the final volume of the gas after expansion.

  • A Ξ” π‘ˆ = 0 , π‘ž = 0 , Ξ” 𝑆 = 0 a n d
  • B Ξ” π‘ˆ > 0 , π‘ž > 0 , Ξ” 𝑆 = 𝑛 ο€½ 𝑉 𝑉  a n d R l n fi n a l i n i t i a l
  • C Ξ” π‘ˆ = 0 , π‘ž > 0 , Ξ” 𝑆 = 𝑛 ο€½ 𝑉 𝑉  a n d R l n fi n a l i n i t i a l
  • D Ξ” π‘ˆ = 0 , π‘ž = 0 , Ξ” 𝑆 = 𝑛 ο€½ 𝑉 𝑉  a n d R l n fi n a l i n i t i a l

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