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5. It is observed that `55.50\ mL` of water at `20°C` completely fills a container to the brim. When the container and the water are heated to `60°C`, `0.35\ g` of water is lost.
(a) What is the coefficient of volume expansion of the container?
(b) What is the most likely material of the container?
The density of water at 60°C is 0.98324 g/mL.
5. It is observed that 55.50\ mL of water at 20°C completely fills a container to the brim. When the container and the water are heated to 60°C, 0.35\ g of water is lost.
(a) What is the coefficient of volume expansion of the container?
(b) What is the most likely material of the container?
The density of water at 60°C is 0.98324 g/mL. `∆V = βV_0∆T`
`β_(contai n er)= 5.0 times 10^(-5) //C°`
Given:
`V_0 = 55.50\ mL`
`T_0 = 20°C`
`T = 60°C`
`m_(lost) = 0.35\ g`
`beta_(H_2O) = 210 times 10^(-6) //C°`
`ρ_(H_2O) = 0.98424 g/mL`
Equation:
`∆V = βV_0∆T`
Solution:
(a)
`V_(lost) = (V_0 +∆V_(H_2O)) - (V_0+∆V_(contai n er))`
`V_(lost) = ∆V_(H_2O)- ∆V_(contai n er)`
`V_(lost) = β_(H_2O)V_0∆T- β_(contai n er)V_0∆T`
`β_(contai n er)V_0∆T= β_(H_2O)V_0∆T-V_(lost)`
`β_(contai n er)= β_(H_2O)-V_(lost)/(V_0∆T)`
`β_(contai n er)= (210 times 10^(-6) //C°)-((0.35\ g)((1\ mL)/(0.98324\ g)))/((55.50\ mL)(60°C - 20°C))`
`β_(contai n er)= 5.0 times 10^(-5) //C°`
(b) the most likely material is copper. |