Does the internal energy of the air, treated as an ideal gas, contained in a room remain constant as the temperature changes between day and night?
Explanation:
The internal energy of an ideal gas can be defined as the sum of the kinetic energy and potential energy of its molecules. In this case, we are considering the air contained in a room. To determine if the internal energy remains constant as the temperature changes between day and night, we need to analyze the behavior of an ideal gas.
According to the ideal gas law, the internal energy of an ideal gas is directly proportional to its temperature. Therefore, as the temperature of the air in the room changes, the internal energy of the gas will also change. However, it is important to note that the internal energy of an ideal gas only depends on its temperature and not on other factors such as pressure or volume.
To mathematically represent this relationship, we can use the equation:
E = n Cv T
Where:
E is the internal energy of the ideal gas
n is the number of moles of the gas
Cv is the molar specific heat at constant volume
T is the temperature of the gas
By analyzing this equation, we can see that the internal energy of the gas is directly proportional to its temperature. Therefore, as the temperature changes between day and night, the internal energy of the air in the room will also change.