The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are gamma1 and gamma2 respectively. If the coefficient of expansion of the vessel A is alpha, the coefficient of linear expansion os the vessel B is
a)alphaxgamma1xgamma2/gamma1+gamma2
b)gamma1-gamma2/2alpha
c)gamma1-gamma2+alpha/3
d)gamma1-gamma2/3+alpha
To determine the coefficient of linear expansion of vessel B, we need to analyze the given information.
Let's break down the problem:
1. The coefficient of apparent expansion of a liquid in vessel A is represented by gamma1.
2. The coefficient of apparent expansion of the same liquid in vessel B is represented by gamma2.
3. The coefficient of expansion (linear expansion) of vessel A is represented by alpha.
To find the coefficient of linear expansion of vessel B, we need to consider how the apparent expansion of the liquid in vessel B is affected by the expansion of the vessel itself (vessel B).
We know that the apparent expansion of the liquid in vessel B is determined by gamma2. This means that when the vessel B expands, it affects the apparent expansion of the liquid.
Since gamma2 represents the apparent expansion of the liquid in vessel B, we need to subtract the effect of the vessel B's expansion to determine the liquid's true expansion. This is where alpha comes into play because it represents the coefficient of expansion for the vessel.
Using this information, we can conclude that the coefficient of linear expansion of vessel B is given by:
Coefficient of linear expansion of vessel B = gamma2 - alpha
Therefore, the correct answer is (gamma1 - gamma2) - alpha, which corresponds to option d) gamma1 - gamma2 / 3 + alpha.