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

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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).

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.