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Ch 20: The Micro/Macro Connection
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 20: The Micro/Macro ConnectionProblem 41
Chapter 20, Problem 41

What is the entropy change of the nitrogen if 250 mL of liquid nitrogen boils away and then warms to 20℃ at constant pressure? The density of liquid nitrogen is 810 kg/m3.

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Step 1: Calculate the mass of the liquid nitrogen. Use the formula \( m = \rho \cdot V \), where \( \rho \) is the density of liquid nitrogen (810 kg/m³) and \( V \) is the volume (250 mL = 0.00025 m³).
Step 2: Determine the entropy change during the phase change (boiling). Use the formula \( \Delta S_{\text{boil}} = \frac{m \cdot L}{T_{\text{boil}}} \), where \( L \) is the latent heat of vaporization for nitrogen (199 kJ/kg) and \( T_{\text{boil}} \) is the boiling temperature of nitrogen in Kelvin (77 K).
Step 3: Calculate the entropy change as the nitrogen gas warms from its boiling point to 20℃. Use the formula \( \Delta S_{\text{warm}} = m \cdot c_p \cdot \ln\left(\frac{T_{\text{final}}}{T_{\text{initial}}}\right) \), where \( c_p \) is the specific heat capacity of nitrogen gas (1.04 kJ/kg·K), \( T_{\text{final}} \) is 20℃ in Kelvin (293 K), and \( T_{\text{initial}} \) is the boiling temperature (77 K).
Step 4: Add the two entropy changes together to find the total entropy change. Use \( \Delta S_{\text{total}} = \Delta S_{\text{boil}} + \Delta S_{\text{warm}} \).
Step 5: Ensure all units are consistent throughout the calculations (e.g., convert kJ to J where necessary) and verify the final expression for \( \Delta S_{\text{total}} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the amount of energy in a physical system that is not available to do work. When a substance undergoes a phase change, such as boiling, its entropy typically increases due to the greater freedom of movement of molecules in the gas phase compared to the liquid phase.
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Phase Change

A phase change refers to the transition of a substance from one state of matter to another, such as from liquid to gas. During this process, energy is absorbed or released, which affects the temperature and entropy of the substance. In the case of liquid nitrogen boiling, it absorbs heat from the surroundings, leading to an increase in entropy as it transitions to the gaseous state.
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Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For nitrogen gas, this value is crucial when calculating the heat absorbed as the gas warms from its boiling point to a specified temperature, such as 20℃. Understanding this concept allows for the calculation of the total heat transfer and the corresponding change in entropy during the warming process.
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Related Practice
Textbook Question

Your calculator can't handle enormous exponents, but we can make sense of large powers of e by converting them to large powers of 10. If we write e = 10α, then eβ = (10α)β = 10αβ. What is the multiplicity of a macrostate with entropy S = 1.0 J/K? Give your answer as a power of 10.

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Textbook Question

The pressure inside a tank of neon is 150 atm. The temperature is 25℃. On average, how many atomic diameters does a neon atom move between collisions?

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Textbook Question

2.0 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy. Which gas has the higher initial temperature?

Textbook Question

A 75 g ice cube at 0℃ is placed on a very large table at 20℃. You can assume that the temperature of the table does not change. As the ice cube melts and then comes to thermal equilibrium, what are the entropy changes of (a) the water, (b) the table, and (c) the universe?

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Textbook Question

Dust particles are ≈ 10 μm in diameter. They are pulverized rock, with ρ ≈ 2500 kg/m³. If you treat dust as an ideal gas, what is the rms speed of a dust particle at 20℃?

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Textbook Question

2.0 mol of helium at 280℃ undergo an isobaric process in which the helium entropy increases by 35 J/K. What is the final temperature of the gas?

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