Question

When a block of iron in mercury at `0^@C,` fraction `K_1`of its volume is submerged, while at the temperature `60^@C,` a fraction `K_2` is seen to be submerged. If the coefficient of volume expansion of iron is `gamma_(Fe)` and that of mercury is `gamma_(Hg),` then the ratio `(K_1)//(K_2)` can be expressed as
A. `(1+60gamma_(Fe))/(1+60gamma_(Hg))`
B. `(1-60gamma_(Fe))/(1+60gamma_(Hg))`
C. `(1-60gamma_(Fe))/(1-60gamma_(Hg))`
D. `(1+60gamma_(Fe))/(1+60gamma_(Hg))`

Answer 1

Correct option is (A) \(\frac{1+60_{γFe}}{1+60_{γHg}}\)

Let V₀​ and V be the volume of the iron block at T = 0°C and 60°C respectively, then we can write 

V = V₀​(1 + 60_γFe​) ........(I)

Let V₀′​ and V′ be the volume of the iron block submerged in the mercury at T = 0°C and 60°C respectively, then we can write 

V′ = V₀′​ (1 + 60_γHg​) ........(II)

Dividing (I) by (II), we get

Answer 2

Correct Answer - A
`W=p_(0)k_(1)V_(0)g=p_(60)k_(2)V_(60)g`
`(k_(1))/(k_(2))=(p_(60))/(p_(0))(V_(60))/(V_(0))`
`=[(p_(0)//(1+gamma_(Hg)xx60))/(p_(0))](V_(0)(1+gamma_(Fe)xx60))/(V_(0))`
`=(1+60gamma_(Fe))/(1+60hgamma_(Hg))`