Suppose the absolute temperature inside a tank of compressed air doubles. What will happen to the pressure inside the tank, if the volume remains constant? Relate temperature to the kinetic energy of the air molecules
To understand how the pressure inside the tank will change when the absolute temperature doubles and the volume remains constant, we need to consider the relationship between temperature and the kinetic energy of air molecules, as well as the ideal gas law.
According to the kinetic theory of gases, the temperature of a gas is proportional to the average kinetic energy of its molecules. As the temperature increases, the average kinetic energy of the molecules also increases.
The ideal gas law, which relates the pressure (P), volume (V), temperature (T), and the number of molecules (n) of a gas, is given by the equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of molecules
R = gas constant
T = absolute temperature
Keeping the volume constant (V constant), we can rearrange the ideal gas law to focus on the relationship between pressure and temperature:
P/T = nR/V
Since the volume is constant, we can simplify the equation to:
P/T = constant
From this relationship, we can infer that as the absolute temperature (T) of the gas doubles, the pressure (P) also doubles if the volume remains constant. This is because temperature and pressure are directly proportional when volume is held constant.
Therefore, when the absolute temperature inside the tank of compressed air doubles, the pressure inside the tank will also double, assuming that the volume remains constant.