Question

A glass flask whose volume is 1000 cm3 at a temperature of 0.300 ∘C is completely filled with mercury at the same temperature. When the flask and mercury are warmed together to a temperature of 52.0 ∘C , a volume of 8.25 cm3 of mercury overflows the flask.

Answer 1

Answer:$2.04\times 10^{-5}/K$

Explanation:

Given

initial volume $V_0=1000 cm^3$

initial Temperature $T_i=0.3^{\circ}C$

Final Temperature $T_f=52^{\circ}C$

Volume of overflow of mercury$=8.25 cm^3$

We know volume expansion of Mercury $\beta _{Hg}=1.80\times 10^{-4} /K$

Volume Expansion of Mercury

$V_f=V_0(1+\beta _{Hg}\Delta T)$

$V_f=1000(1+1.80\times 10^{-4}\times 51.7)$

$V_f=1009.306 cm^3$

therefore volume Expansion of flask

$V_f-8.25=1009.306-8.25=1001.056 cm^3$

Volume Expansion of Glass

$V_f'=V_0(1+\beta _{glass}\Delta T)$

$1001.056=1000(1+\beta _{glass}\times 51.7)$

$1.001056=1+\beta _{glass}\times 51.7$

$\beta _{glass}\times 51.7=0.001056$

$\beta _{glass}=\frac{0.001056}{51.7}=2.04\times 10^{-5}/K$