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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 28
Chapter 20, Problem 28

A 6.0 m ✕ 8.0 m ✕ 3.0 m room contains air at 20℃. What is the room's thermal energy?

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Determine the volume of the room by multiplying its dimensions: \( V = 6.0 \times 8.0 \times 3.0 \, \text{m}^3 \).
Calculate the mass of the air in the room using the density of air at 20℃ (approximately \( \rho = 1.204 \; \text{kg/m}^3 \)): \( m = \rho \cdot V \).
Use the specific heat capacity of air at constant pressure (\( c_p \approx 1005 \; \text{J/(kg·K)} \)) to calculate the thermal energy. The formula for thermal energy is \( Q = m \cdot c_p \cdot \Delta T \), where \( \Delta T \) is the temperature in Kelvin.
Convert the given temperature from Celsius to Kelvin using \( T_K = T_C + 273.15 \). For this problem, \( \Delta T = 20 + 273.15 \).
Substitute the values for \( m \), \( c_p \), and \( \Delta T \) into the formula \( Q = m \cdot c_p \cdot \Delta T \) to find the thermal energy of the air in the room.

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Key Concepts

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

Thermal Energy

Thermal energy is the total kinetic energy of the particles in a substance due to their motion. In the context of a room filled with air, it is influenced by the temperature and the number of air molecules present. The higher the temperature, the greater the average kinetic energy of the air molecules, leading to increased thermal energy.
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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 air, this value is essential in calculating the thermal energy, as it determines how much energy is needed to change the temperature of the air in the room. The specific heat capacity of air at constant pressure is approximately 1005 J/(kg·K).
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Volume and Density

The volume of a room and the density of the air within it are critical for calculating thermal energy. The volume of the room (6.0 m × 8.0 m × 3.0 m) helps determine the total mass of air present, as density relates mass to volume. The density of air at 20℃ is about 1.204 kg/m³, which allows for the calculation of the total mass of air in the room, necessary for finding the thermal energy.
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Related Practice
Textbook Question

The vibrational modes of molecular nitrogen are 'frozen out' at room temperature but become active at temperatures above ≈1500 K. The temperature in the combustion chamber of a jet engine can reach 2000 K, so an engineering analysis of combustion requires knowing the thermal properties of materials at these temperatures. What is the expected specific heat ratio γ for nitrogen at 2000 K?

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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

The rms speed of the atoms in a 2.0 g sample of helium gas is 700 m/s. What is the thermal energy of the gas?

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Textbook Question

Liquid helium boils at 4.2 K. In a flask, the helium gas above the boiling liquid is at the same temperature. What are (a) the mean free path in the gas, (b) the rms speed of the atoms, and (c) the average energy per atom?

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Textbook Question

The thermal energy of 1.0 mol of a substance is increased by 1.0 J. What is the temperature change if the system is (a) a monatomic gas, (b) a diatomic gas, and (c) a solid?

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Textbook Question

1.0 mol of argon has 3100 J of thermal energy. What is the gas temperature in °C?

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