Suppose a sample of gas is trapped in a container that cannot change size. Now suppose the temperature of the gas is doubled. The pressure will be _________.
Responses
A halved
B doubled
The correct response is B) doubled.
According to the ideal gas law, the pressure (P) of a gas is directly proportional to its temperature (T) when volume (V) and the number of moles (n) are constant. Mathematically, this relationship can be expressed as:
P1/T1 = P2/T2
If the temperature is doubled (T2 = 2T1), then the pressure will also double (P2 = 2P1).
To determine how the pressure of the gas changes when the temperature is doubled, we can use the ideal gas law equation: PV = nRT.
In this equation, P represents pressure, V represents volume, n represents the number of gas particles (in moles), R is the ideal gas constant, and T represents temperature.
Since the volume of the container is fixed and cannot change size, we can simplify the equation to P = (nR/V) * T.
Now, let's analyze the situation. We are told that the temperature is doubled. If we plug this into the equation, we get P' = (nR/V) * 2T, where P' represents the new pressure.
By comparing the original pressure equation P = (nR/V) * T to the new equation P' = (nR/V) * 2T, we can see that the pressure has doubled when the temperature is doubled.
Therefore, the correct answer is B) doubled.