Certainly!
According to the ideal gas law, the relationship between pressure (P), volume (V), number of moles (n), the gas constant (R), and temperature (T) is given by:
[tex]\[ PV = nRT \][/tex]
In the problem, it is specified that the gas has experienced a small increase in volume (V) while the pressure (P) and the number of moles (n) are maintained constant.
Given the relationship from the ideal gas law, if we isolate temperature (T), we get:
[tex]\[ T = \frac{PV}{nR} \][/tex]
Since P and n are constant, the temperature (T) is directly proportional to the volume (V). This can be simplified to:
[tex]\[ V \propto T \][/tex]
This means that if there is an increase in volume, there must also be an increase in temperature to maintain the proportionality defined by the ideal gas law.
Since the increase in volume is described as "small," the corresponding increase in temperature will also be slight. Therefore, the correct conclusion is:
"It has increased slightly."
This means the temperature of the gas has increased slightly due to the small increase in volume while keeping the pressure and number of moles constant.
