Question 568: Thermodynamics & KTG

Question

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

Integer / Numeric Answer Type