When a block of iron floats in mercury at 0oC, a fraction k1, of its volume is submerged, while at the temperature 600 C, a fraction k2, is submerged. If thecoefficient of volume expansion of iron is γFe and that of mercury isγFe , then the ratio ,k1 / k2 can be expressed as

let M be the mass of iron block and V its volume. ThenMg=VρFe(0)g=k1VρHg or ρFe(0)=k1ρHg(0) and Mg=VρFe(60)g=k2VρHg(60)g or ρFe(60)=k2ρHg(60) ∴ ρFe(0)ρFe(60)=k1k2×ρHg(0)ρHg(60)  Now  ρFe(60)=ρFe(0)1+60γFe  and ρHg(60)=ρHg(0)1+60γHg ∴ k1k2=ρFe(0)ρFe(60)×ρHg(60)ρHg(0)=1+60γFe1+60γHg