The density of water at 21 degrees C is 0.997992 g/mL. The density of water at 22 degrees C is 0.997770 g/mL. What is the density of water if the room temperature is 21.3 degrees C??
So I would just multiply 30 percent of the density at 21 degrees C but I'm stuck on how to find the density specifically at 21.3 degrees C?
To find the density of water at 21.3 degrees Celsius, you can use interpolation. Interpolation is a method of estimating a value within a range of known values using existing data points.
Here are the steps to interpolate the density at 21.3 degrees Celsius:
1. Calculate the difference between the known temperatures:
ΔT = T2 - T1 = 22 - 21 = 1 degree Celsius.
2. Calculate the difference between the known densities:
ΔD = D2 - D1 = 0.997770 g/mL - 0.997992 g/mL = -0.000222 g/mL (note the negative sign indicates decrease in density).
3. Calculate the temperature difference from the known temperature to the desired temperature:
Δt = T - T1 = 21.3 - 21 = 0.3 degree Celsius.
4. Apply the formula for interpolation:
Density at the desired temperature (D') = D1 + (ΔD / ΔT) * Δt
Plugging in the values, we have:
Density at 21.3 degrees C = 0.997992 g/mL + (-0.000222 g/mL / 1 degree Celsius) * 0.3 degree Celsius
Simplifying the equation:
Density at 21.3 degrees C = 0.997992 g/mL - 0.0000666 g/mL
The density at 21.3 degrees C is approximately 0.997925 g/mL.
Therefore, to find the density of water at 21.3 degrees C, you would subtract 0.0000666 g/mL from the known density at 21 degrees C (0.997992 g/mL).