Question

The density of mercury is 13.6 g cm?3 at 0?C and its coefficient of cubical expansion is 1.82�10?4 ?C?1. Calculate the density of mercury at 50?C

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Answer 1

${\red{\underline{\boxed{\underline{\sf{GIVEN:}}}}}}$

${\tt{mass\: of \:the\: mercury \:= \:13.6gm}}$ .

${\tt{Coefficient \:of\: cubical\: expansion \:α\: =}}$ ${\tt{1.82×10^-4°C^-1 }}$ .

$\green{\underline{\boxed{\underline{\sf{SOLUTION :}}}}}$

${\tt{consider :}}$

${\boxed{\red{\sf{Volume = 1cm^3}}}}$

${\tt{When \:mercury\: is \:heated\: to \:500°C\: then\: change\: in \:the\: mass,}}$

${\boxed{\red{\sf{ΔV = V α ΔT}}}}$

${\tt{ΔV = 1 × 1.82×10^-4× 50}}$

${\boxed{\green{\sf{ΔV = 9.1 ×10^-3 cm^3}}}}$

${\tt{New\: volume \:can \:be\: calculated\: as,}}$

${\boxed{\red{\sf{V1 = V + ΔV}}}}$

${\tt{V1 = 1 + 9.1×10^-3}}$

${\boxed{\green{\sf{V1 = 1.0091 cm^3}}}}$

${\tt{New\: volume\: can\: be\: calculated \:as,}}$

${\boxed{\red{\sf{ρ = m/V1}}}}$

${\tt{ρ = 13.6/1.0091}}$

${\boxed{\purple{\sf{ρ = 13.48 gcm .}}}}$

Hence, the density of mercury at 50°c is 13.48gcm.