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* 10^(-5)/K`

Step-by-step 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* 10^(-4) /K`

Volume Expansion of Mercury

`V_f=V_0(1+\beta _(Hg)\Delta T)`

`V_f=1000(1+1.80* 10^(-4)* 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)* 51.7)`

`1.001056=1+\beta _(glass)* 51.7`

`\beta _(glass)* 51.7=0.001056`

`\beta _(glass)=(0.001056)/(51.7)=2.04* 10^(-5)/K`