The volume expansivity of a gas under constant pressure is `0.0037`. Calculate its volume at- `100^(@)C` if its volume at `100^(@)C` is `685 cm^(3)`.

Explanation

The volume expansivity of a gas means increase or decrease in volume per degree rise or fall in temperature of its volume at `0^(@)C`. Therefore,
`V_(t)=V_(0)+0.0037xxV_(0)xxt=V_(0)(1+0.0037t)`
At `100^(@)C`, `V_(100^(@)C)=V_(0)(1+0.0037xx100)`
`685cm^(3)=V_(0)(1+0.37) (V_(100^(@)C)=685cm^(3) given)`
`:, V_(0)=(685)/(1.37)=500cm^(3)`
Therefore, volume at `-100^(@)C` is
`V_(-100^(@)C)=V_(0)[1+0.0037xx(-100)]`
`=500[1+0.0037xx(-100)]=315cm^(3)`
Hence, volume at `-100^(@)C` is `V_(-100)=315cm^(3)`.