If the temperature and pressure of an ideal gas are tripled, what is the ratio of the new volume to the initial volume?
Question
If the temperature and pressure of an ideal gas are tripled, what is the ratio of the new volume to the initial volume?
Solution
The question is based on the ideal gas law, which states that the product of the pressure (P) and volume (V) of a gas is directly proportional to the product of the number of moles (n) of the gas and the temperature (T) in Kelvin. This can be written as:
PV = nRT
where R is the ideal gas constant.
If the temperature and pressure are tripled, the equation becomes:
3P * V2 = n * 3R * T
We can simplify this to:
V2 = (nRT) / (3P)
Since nRT is equal to PV (from the original ideal gas law), we can substitute PV in for nRT:
V2 = PV / (3P)
The P's cancel out, leaving:
V2 = V / 3
So, the ratio of the new volume (V2) to the initial volume (V) is 1/3.
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