The density of a substance at 100 degrees centigrade is 1.22 g/(cm^3) and at 140 degrees centigrade is 0.95 g/(cm^3). Estimate the density at 115 degrees centigrade using linear interpolation. Observe significant digits.
D1 = 1.22g/cm^3, T1 = 100oC.
D2 = 0.95g/cm^3, T2 = 140oC.
D3 = density @ 115oC.
T.C. = (D2- D1)/(T2 - T1) = (0.95-1.22)/(140-100) = -0.00675/oC. = Temp.
coefficient.
D3 = D1 + (T.C.)*(T3-T1)D1 = 1.22 + (-0.00675)*(115-100) = 1.22 - 0.10125 = 1.11875 g/cm^3.
To estimate the density at 115 degrees Celsius using linear interpolation, we can use the following formula:
Density at 115°C = Density at 100°C + (Density at 140°C - Density at 100°C) * (115°C - 100°C) / (140°C - 100°C)
Let's substitute the given values into the formula:
Density at 115°C = 1.22 g/(cm^3) + (0.95 g/(cm^3) - 1.22 g/(cm^3)) * (115°C - 100°C) / (140°C - 100°C)
First, let's calculate the numerator of the fraction:
0.95 g/(cm^3) - 1.22 g/(cm^3) = -0.27 g/(cm^3)
Now, let's calculate the denominator of the fraction:
140°C - 100°C = 40°C
Now, let's substitute these values back into the equation:
Density at 115°C = 1.22 g/(cm^3) + (-0.27 g/(cm^3)) * (115°C - 100°C) / 40°C
Density at 115°C = 1.22 g/(cm^3) + (-0.27 g/(cm^3)) * 15°C / 40°C
Density at 115°C = 1.22 g/(cm^3) + (-0.405 g/(cm^3))
Density at 115°C = 0.815 g/(cm^3)
Therefore, the estimated density of the substance at 115 degrees Celsius is approximately 0.815 g/(cm^3), observing significant digits.