Question 2
Marks : +2 | -2
Pass Ratio : 33%
Mass of a substance is changing with respect to its volume as m = -v3 + 3v2 -2v, what is the maximum specific gravity of the substance between v = 1 m3 and v = 2 m3? (Density of reference substance = 0.25 kg/m3)
Explanation: Density of substance D = m/v = -v2 + 3v – 2, => Specific gravity of substance S = D/0.25 = 4(-v2 + 3v – 2), => dS/dv = 4(-2v + 3) = 0, => v = 1.5, => S is maximum at v = 1.5, => maximum specific gravity = 4(-1.52 + 3*1.5 – 2) = 1.
Question 3
Marks : +2 | -2
Pass Ratio : 33%
API gravity is necessary for the calculation of specific gravity of petroleum products, because
Explanation: Since volume of petroleum products changes significantly with temperature, that means density of petroleum products changes significantly with temperature, so that’s why specific gravity of petroleum products changes with temperature, and that’s why API gravity is required.
Question 8
Marks : +2 | -2
Pass Ratio : 33%
It is necessary to mention the temperature at which specific gravity is calculated, because
Explanation: Since the volume of the substance changes with temperature, which means density of the substance changes with temperature, that’s why it is required to mention the temperature at which specific gravity is calculated.
Question 9
Marks : +2 | -2
Pass Ratio : 33%
What is the average mass of a substance with specific gravity 10, and its volume varies with time as V = t/500, from t = 2, to t = 0 seconds? (Density of water = 1000 kg/m3)
Explanation: Density of substance = 10 * 1000 = 10000 kg/m3, => mass of substance = 10000*t/500 = 20t, => average mass = (1/2)∫20t = 5t2 = 5(22 – 02) = 20.