Question

A liquid occupies half of a vessel at a
particular temperature. The volume of the
unoccupied part remains constant at all
temperatures. If a and are the
coefficients of linear and real expansions of
a vessel and liquid, then gama=​

Answer 1

Let us suppose the volume of vessel be V,so volume occupied by liquid is V2.Now, If we increase the temperature by ∆T and a is the linear expansion of vessel,then 3a is the volumic expansion of vessel.Now, new volume of vessel=V1+3a∆Tand new volume of liquid=V21+b∆TAccording to question,V1+3a∆T-V21+b∆T=kwhere k=constantV1+3a∆T-V21+b∆T=V2V+3aV∆T-V2-V2×b∆T=V2V1+3a∆T-12-12b∆T=V21+3a∆T-12-12b∆T=121+3a∆T-12b∆T=13a∆T=12b∆Tb=6