Question

A vessel of volume 'V' is half - filled with a liquid “A” of volume coefficient of expansion a1 and the other half with a liquid B of volume coefficient a2 at
00C. If the vessel has negligible coefficient of expansion, the mass of liquid that over flows when it heated to 100C is (density of A = d, density of B =
0.8d)
(A) Vd(a1+a2)
(B) 4Vd(a1+a2)
(C) 4Vd [(a 1+a2)2]
(D) 4Vd(a1-a2)​

Answer 1

Explanation:

.......................

Answer 2

Answer:

Mass of liquid that is overflown is $4Vd(a_{1}+a_{2})$

Explanation:

Given volume of liquid A =  volume of liquid B = $\frac{V}{2}$

          volume coefficient of expansion of liquid A is $a_{1}$

          volume coefficient of expansion of liquid B is $a_{2}$  

          Temperature difference, $\Delta T=10^{o} C$

          density of liquid A =d

          density of liquid B, $\rho = 0.8d$

Volume expansion is

                       $\Delta V=\rho V_{0} \Delta T$

                       $\Delta V=a_{1} \times \frac{V}{2} \times 10+a_{2} \times \frac{V}{2} \times 10$

                              $=5V(a_{1}+a_{2})$

As density of liquid B is less, it is lighter than A and hence overflows after expansion.

Mass of the liquid overflown is $m=\rho\Delta V$

                          $m=0.8d \times 5V(a_{1}+a_{2})$

                               $=4Vd(a_{1}+a_{2})$

Mass of liquid B that is overflown is $4Vd(a_{1}+a_{2})$

So, the correct is option B.