Question

The density of water at 4ºC is 1.00 x 103 kg/m3. What is water's density at 82ºC? Assume that the water's coefficient of volume expansion is constant. Enter your answer in kg/m3, without units, to the nearest whole number.

Answer 1

Answer:

Density of water at $T = 82^0 C , \rho = 983.308 kg/m^3$

Explanation:

The relationship between density and temperature is shown below:

$\rho_1 = \rho_0 [ 1- \beta \Delta T ]$

Where,

$\rho_1$  is the density at temperature $T_1$

$\rho_0$  is the density at temperature $T_0$

$\beta$ is the coefficient of volume expansion

$\Delta T$ is the change in temperature which is:

$\Delta T = {T_1} -{T_0}$

Given,

$T_0 = 4^0 C$

$\rho_0 = 1.00\times 10^3 kg/m^3$

$T_1 = 82^0 C$

$\Delta T = (82 -4) ^0 C =78 ^0 C$

$\rho_1 = ?$

Also,

$\beta for water = 0.000214 ^0C^{-1}$

So,

$\rho_1 is:$

$\rho_1 = 1.00\times 10^3 kg/m^3[1 - 0.000214 ^0C^{-1} \times 78^0 C ]$

$\rho_1 = 983.308 kg/m^3$