crude oil is contained in an iron cylindrical tank whose height is 6m and diameter of the base is 5m. at 0c, the level of crude oil is 20cm below the brim. at what temp will the oil start to over flow from the tank

309k

To determine at what temperature the oil will start to overflow from the tank, we need to consider the expansion of the oil due to temperature changes. When the oil expands, its volume increases, which can cause it to overflow from the tank.

First, let's calculate the current volume of the oil in the tank. The tank is in the shape of a cylinder, so we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

Given:
Height of the tank (h) = 6m
Diameter of the base (2r) = 5m
Radius of the base (r) = 5m / 2 = 2.5m

Substituting the values into the formula:

Volume = π * (2.5m)^2 * 6m
Volume ≈ 117.81 m^3

Now, let's calculate the volume at which the oil would start overflowing from the tank. Since the oil level is currently 20cm below the brim, we need to calculate the additional volume that would cause it to overflow.

Additional Volume = π * (2.5m)^2 * (20cm + 6m)
Additional Volume ≈ 47.12 m^3

To find the temperature at which the oil will start to overflow from the tank, we need to consider the coefficient of thermal expansion (CTE) of the oil. The CTE measures how much the volume of a material expands or contracts with a change in temperature.

The exact CTE value for crude oil depends on its specific composition, but as a general approximation, we can assume a CTE of around 0.00095 per °C.

Finally, we can calculate the temperature change needed for the additional volume of the oil:

Temperature Change = Additional Volume / (Volume * CTE)

Temperature Change ≈ 47.12 m^3 / (117.81 m^3 * 0.00095 per °C)
Temperature Change ≈ 41225.1 °C

Therefore, at a temperature increase of approximately 41225.1 °C, the crude oil will start to overflow from the tank. Please note that this calculation assumes a linear relationship between temperature and volume expansion, which may not always be precise in reality.