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3. The density of water at `4°C` is `1.00 times 10^3\ kg//m^3`. What is water's density at `94°C`?
3. The density of water at 4°C is 1.00 times 10^3\ kg//m^3. What is water's density at 94°C? `ρ = m/V`
`∆V = betaV_0∆T `
`ρ_(94°C) = 981\ kg//m^3`
Given:
`ρ_(4°C)=1.00 times 10^3 kg//m^3`
Known:
`beta_(H_20) = 210 times 10^(-6) //C°`
Equation:
`∆V = betaV_0∆T `
Solution:
`ρ_(4°C) = m/V_(4°C)`
`∆V = betaV_(4°C)∆T`
`=>`
`ρ_(94°C) = m/(V_(4°C)+∆V) = m/(V_(4°C)+betaV_(4°C)∆T)`
`ρ_(94°C) = m/((V_(4°C)(1+beta∆T))`
`ρ_(94°C) = ρ_(4°C)/(1+beta∆T)`
`ρ_(94°C) = (1.00 times 10^3 kg//m^3)/(1+(210 times 10^(-6) //C°)(94°C-4°C))`
`ρ_(94°C) = 981\ kg//m^3` |