An ideal gas is initially at temperature T and volume V. Its volume is increased by `DeltaV` due to an increase in temperature `DeltaT,` pressure remaining constant. The quantity `delta=(DeltaV)/(VDeltaT)` varies with temperature as

Options

A.
B.
C.
D.

Answer

C

Explanation

For a given mass of gas at constant pressure.
`(V)/(T)=` constant `therefore (V+DeltaV)/(T+DeltaT)=(V)/(T)`
or `VT+VDeltaT=VT+TDeltaV` or `VDeltaT=TDeltaV`
or `(1)/(T)=(DeltaV)/(VDeltaT)` or `(1)/(T)=delta` or `deltaT=1`
The equation represents a rectangular hyperbola of the form `xy=c^(2)`.
Hence the `delta-T` variation is represented by graph (c).