How will the volume of a fixed sample of gas change if its pressure is doubled and the Kelvin temperature is doubled?
a)the change cannot be determined without more specific information
b)it will decrease by a factor of 2
c)it will increase by a factor of 4
d)no change
e)it will double
Use PV = nRT OR remember Boyle's Law and Charles' Law.
d no change
Increase by factor of 4
To determine how the volume of a fixed sample of gas will change when its pressure is doubled and the Kelvin temperature is doubled, we can use the combined gas law equation: PV = nRT.
In this equation:
P represents the pressure of the gas,
V represents the volume of the gas,
n represents the number of moles of gas,
R is the ideal gas constant, and
T represents the Kelvin temperature of the gas.
Since we have a fixed sample of gas, the number of moles (n) remains constant.
When the pressure is doubled and the temperature is doubled, we can express these changes as:
P' = 2P (pressure doubled)
T' = 2T (Kelvin temperature doubled)
Using the combined gas law equation, we can compare the initial state (P, V, and T) with the final state (P', V', and T'):
(P)(V) / (n)(T) = (P')(V') / (n)(T')
Substituting the given values, we have:
(P)(V) / (n)(T) = (2P)(V') / (n)(2T)
Simplifying, we see that the n's cancel out:
(V) / (T) = (2)(V') / (2T)
Now, let's rearrange the equation to solve for V':
V' = (V) / (T) * (2T)
Since the temperature (T) and 2T are on both sides of the equation, they cancel out:
V' = V
From the equation, we can see that the volume of the fixed sample of gas (V') remains the same as the initial volume (V). Therefore, the answer is (d) no change.
So, to recap:
When the pressure of a fixed sample of gas is doubled and the Kelvin temperature is doubled, the volume of the gas does not change.