Worksheet: Heat Capacity

In this worksheet, we will practice calculating the heat capacity of an object from the amount of heat exchanged and the change in temperature.

Q1:

The heat capacity of a substance can be measured under either constant volume or constant pressure conditions. Which of the following sets of relationships between 𝐢 (heat capacity under constant volume conditions) and 𝐢 (heat capacity under constant pressure conditions) are always true?

  • A 𝐢 ( ) β‰ˆ 𝐢 ( )   g a s s o l i d and 𝐢()β‰ˆπΆ()οŒο“liquidliquid
  • B 𝐢  approaches a value of 0 as the sample temperature approaches 0 K but increases without bound as the sample temperature is increased.
  • C 𝐢 ( ) > 𝐢 ( ) > 𝐢 ( )    g a s l i q u i d s o l i d and 𝐢>πΆο“οŒ in all phases
  • D 𝐢 ( ) > 𝐢 ( )   g a s g a s , 𝐢 ( ) β‰ˆ 𝐢 ( )   s o l i d s o l i d , and 𝐢()≫𝐢()gassolid

Q2:

Suppose 2 moles of water at 333 K are added to 4 moles of water at 293 K. What would the entropy change associated with this process be, assuming that there is no exchange of heat with the surroundings? (The heat capacity of water is 𝐢=75.3/β‹…οŒοŽ•ο‰JKmol and may be considered to be independent of temperature.)

Q3:

Two 1-mole blocks of aluminum, one at 273 K and the other at 373 K, are brought into thermal contact. What will the temperature of the two blocks be when they have reached thermal equilibrium? What will the total entropy change (Δ𝑆)tot that accompanies the thermal equilibration process be? Assume that the two blocks of aluminum are in a container with walls that keep them completely isolated from outside surroundings, and take the heat capacity of the aluminum blocks to be 𝐢=24.35/β‹…οŒοŽ•ο‰JKmol.

  • A 𝑇 = 3 7 3 e q u i l K and Δ𝑆=6.21/totJK
  • B 𝑇 = 3 2 3 e q u i l K and Δ𝑆=0tot
  • C 𝑇 = 3 2 3 e q u i l K and Δ𝑆=0.59/totJK
  • D 𝑇 = 3 2 3 e q u i l K and Δ𝑆=βˆ’0.59/totJK

Q4:

Complete the following sentence: The Joule–Thomson experiment involves an isenthalpic thermodynamic process. The measurements performed in this experiment permit evaluation of the quantity πœ‡=ο€½πœ•π‘‡πœ•π‘ƒο‰β‰ˆΞ”π‘‡Ξ”π‘ƒοŒ©οŠ±οŒ³οŒ§. The observed values of πœ‡οŒ©οŠ±οŒ³ are .

  • A = 0 in all nonideal gases
  • B> 0 only for gases that exhibit ideal-gas 𝑃‐𝑉‐𝑇 behavior
  • Cindependent of the initial temperature and pressure of the gas undergoing the Joule–Thomson expansion process
  • D> 0 for nearly all gases
  • E< 0 for nearly all gases

Q5:

Consider a 2 mol sample of an ideal gas, with a molar heat capacity 𝐢=12.5/β‹…ο“οŽ•ο‰JKmol, confined to a volume of 5 dm3 at a temperature of 300 K. If this gas sample is heated to 373 K and its volume is allowed to expand to 10 dm3, how much heat (π‘ž) is required to perform this process, and what is the entropy change (of the gas) that accompanies this process?

  • A Ξ” 𝑆 = 1 1 . 5 3 / J K ; π‘ž = 1 , 8 2 5 J
  • B Ξ” 𝑆 = 1 6 . 9 7 / J K ; π‘ž = 1 , 8 2 5 J
  • C Ξ” 𝑆 = 1 6 . 9 7 / J K ; the value of π‘ž depends on whether the process is carried out reversibly or irreversibly.
  • D Ξ” 𝑆 = 5 . 4 4 / J K ; π‘ž = 1 , 8 2 5 J

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