Heat and Thermodynamics 3 Question 13
13. A sinker of weight $w _0$ has an apparent weight $w _1$ when placed in a liquid at a temperature $T _1$ and $w _2$ when weighed in the same liquid at a temperature $T _2$. The coefficient of cubical expansion of the material of the sinker is $\beta$. What is the coefficient of volume expansion of the liquid?
(1978)
schematically? (Assume the emissivity of both the beakers to be the same)
(2019 Main, 8 April I) (a)
(c)
(b)
(d)
Show Answer
Solution:
- $\frac{d Q}{d t}=L\left(\frac{d m}{d t}\right)$
or $\quad \frac{\text { Temperature difference }}{\text { Thermal resistance }}=L\left(\frac{d m}{d t}\right)$
$$ \begin{array}{rlrl} \text { or } & & \frac{d m}{d t} & \propto \frac{1}{\text { Thermal resistance }} \\ \Rightarrow & q & \propto \frac{1}{R} \end{array} $$
In the first case rods are in parallel and thermal resistance is $\frac{R}{2}$ while in second case rods are in series and thermal resistance is $2 R$.
$$ \frac{q _1}{q _2}=\frac{2 R}{R / 2}=\frac{4}{1} $$
