Question 623: Thermodynamics & KTG

Question

A bakelite beaker has volume capacity of 500 cc at 30oC. When it is partially filled with Vm
 volume
(at 30oC) of mercury, it is found that the unfilled volume of the beaker remains constant as
temperature is varied. If $$\gamma $$(beaker) = 6 × 10–6 oC–1 and $$\gamma $$(mercury) = 1.5 × 10–4 oC–1, where $$\gamma $$ is the
coefficient of volume expansion, then Vm
 (in cc) is close to ____.

Accepted Answer

$$\Delta $$V = V$$\gamma $$$$\Delta $$T
$$ 	herefore $$ V
1
$$\gamma $$
1
= V
2
$$\gamma $$
2
$$ \Rightarrow $$ 500 $$ 	imes $$ 6 $$ 	imes $$ 10
-6
= V
m
$$ 	imes $$ 1.5 $$ 	imes $$ 10
-4
$$ \Rightarrow $$ V
m
= $${{500 	imes 6 	imes {{10}^{ - 6}}} \over {1.5 	imes {{10}^{ - 4}}}}$$
$$ \Rightarrow $$ V
m
= 20 cc

Thermodynamics & KTG

Choose the correct answer: