The Volume of the gas will decrease when a sample of gas from a hot area to a cooler area assuming that there is no change in pressure and that no gas is lost in the process.
The equation of an ideal gas is mentioned below;
PV = nRT
Let us assume that there is no change in pressure and that no gas is lost in the process of gas transfer. So, we can write
Pressure = P = Constant
Number of moles = n = Constant
R = Gas Constant
So, we can write the relation between the temperature and volume of gas as
T ∝ V
We are transferring a sample of gas from a hot area to a cooler area i.e., Temperature is decreasing. So, the Volume of the gas will also decrease.
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