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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.
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