20.0L of a sample of gas at 25 Celsius is compressed to 5L. What is the final temperature in CELSIUS assuming there is no pressure change?
i got the answer to be 6.3 degree. but am not sure because i didn't change convert 25 degree to Kelvin since it said i should give the answer in Celsius. if i change it to Kelvin and subtract my final answer from 273.15, my answer will be -198.6. am confused. can anyone explain in simpler terms?
This is a Charles's law application. To do problems of this sort you must first convert the temperature to kelvin. K = 273.15 + degrees celsius. After you finish working the problem then convert the answer which you get from Kelvin back celsius.
In this case you have an initial volume of 20 L, a final volume of 5 liters, and an initial temperature of 25 C or 298.15 K.
In equation form you have:
20/298.15 = 5/T2
rearranging to solve for T2, you get:
T2 = 298.15 x 5 /20
T2 = 74.54 K
Converting to degrees celsius you get 74.54 - 273.15 = -198.6 degrees celsius.
So you did it correctly. What this illustrates is how much you have to cool a gas to decrease its volume. You may have seen the demonstration where liquid nitrogen (77 K) is poured over an inflated balloon and the balloon becomes almost flat. This problem is comparable to that type of low temperature.
As long as you convert to Kelvin first, then do the problem, and then convert back to celsius you will continue to get the correct answer.
As per the Universal Gas Law:
PV/T = Constant for a given mass of a gas
P = Pressure
V = Volume
T = Absolute temperature
In the question the gas is compressed from Initial Volume
V1 = 20 l
to Final Volume
V2 = 5 l
The Initial and final pressure remains same: That is
P1 = P2 = P
Initial temperature = T1 = 25 degrees Celsius = 25 + 273.15 = 298.15 degrees Kelvin.
Applying the universal gas law:
P1V1/T1 = P2V2/T2
==> PV1/T1 = PV2/T2
==> V1/T1 = V2/T2
==> T2 = (V2/V1)T1
Substituting the values of V1, V2 and T1 in above equation:
T2 = (5/20)(298.15) = 74.5375 degree Kelvin
= 74.5375 - 273.15 = -198.6125 degrees Celsius
Final Temperature = -198.6125 degrees Celsius