The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is

Options

A. `(1)/(7)`
B. `(7)/(6)`
C. `(6)/(7)`
D. None of these

Answer

B

Explanation

Given `gamma_("liquid") = 7 gamm_("vessel")`
`Delta V_("Absolute") = gamma_("liquid") V Delta T= 7 gamma_("vessel") .V Delta T` …(i)
`Delta V_("vessel") = gamma_("vessel").V.Delta T`
`Delta V_("Apparent") = Delta V_("liquid") - DeltaV_("vessel")`
`= V. Delta (gamma_("liquid") - gamma_("vessel")) = V.Delta T (7gamma_("vessel") - gamma_("vessel"))`
`rArr Delta V_("Apparent")= V.Delta T (6gamma_("vessel"))` ...(ii)
Equation (i) divided by equation (ii), we get,
`(Delta V_("Absolute"))/(Delta V_("Apparent")) = (gamma_("Absolute"))/(gamma_("Apparent"))= (7gamma_("vessel").V Delta T)/(6 gamma_("vessel").V Delta T)= (7)/(6)`
`rArr` b is correct