Certain amount of gas occupies 400 ml at 17 degree C. At what temperature would the volume be reduced to half.
Let us assume the gas can be considered to be an ideal gas. The relation between pressure P, temperature T and volume V of an ideal gas is: P*V = n*R*T, where n is the amount of gas in moles and R is a constant.
Here, the amount of gas is not changing and as R is a constant we can write the ideal gas equation as P*V/T = constant
V1 = 400 ml and T1 = 17 C or 290 K.
We need to determine the change in temperature to decrease the volume by half. The pressure is assumed to remain constant in both the cases.
400/290 = (400/2)/T2
=> T2 = 290/2
=> 145 K
or -128 degree Celsius
The gas has to be cooled to -128 degree Celsius to reduce the volume to half.