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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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 20: The Micro/Macro ConnectionProblema 28
Capitolo 20, Problema 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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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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Volume Thermal Expansion

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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Specific Heat & Temperature Changes

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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Problems with Mass, Volume, & Density
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