crude oil is contained in an iron cylindrical tank whose heogth is 6m and the diameter of the base is 5m. at 0 degree celcius , the level of crude oil is 20cm below the brim. At what temperature will the crude oil start to overflow from the tank? the thermal expansion
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To calculate the temperature at which the crude oil will start to overflow from the tank, we need to consider the thermal expansion of both the oil and the tank material.
First, let's find the volume of the cylindrical tank:
The radius of the base (r) is half the diameter, so r = 5m / 2 = 2.5m.
The height (h) of the tank is given as 6m.
The formula for the volume (V) of a cylinder is: V = πr²h.
Plugging in the values, we get:
V = π * (2.5m)² * 6m = π * 6.25m² * 6m ≈ 117.81m³.
Next, let's calculate the volume of the space left for the oil to fill before overflowing:
The height of the oil is given as 20cm, which is equivalent to 0.2m.
The remaining height of the tank (h_remaining) is the total height minus the height of the oil: h_remaining = 6m - 0.2m = 5.8m.
The volume of the remaining space (V_remaining) is:
V_remaining = π * (2.5m)² * 5.8m ≈ 106.84m³.
Now, let's consider the thermal expansion of both the oil and the tank material. Crude oil has a coefficient of thermal expansion (β) of approximately 0.0008 per degree Celsius. The tank material, iron, has a coefficient of thermal expansion of approximately 0.000012 per degree Celsius.
Let's assume the final temperature at which the oil will overflow is represented by T (in degrees Celsius). At this temperature, the combined volume of the oil and the remaining space in the tank will equal the volume of the tank.
Taking into account the expansion of the oil and the tank material, the equation becomes:
117.81m³ + (117.81m³ * β * T) = 106.84m³ + (106.84m³ * 0.000012 * T).
Simplifying the equation:
117.81m³ + 0.094248m³T = 106.84m³ + 0.00128208m³T.
Rearranging the equation:
0.09296592m³T = 10.97m³.
Solving for T:
T = 10.97m³ / 0.09296592m³ ≈ 118.06°C.
Therefore, the crude oil will start to overflow from the tank at a temperature of approximately 118.06 degrees Celsius.
To determine at what temperature the crude oil will start to overflow from the tank due to thermal expansion, we need to calculate the expansion of the oil and compare it to the remaining space in the tank.
First, let's calculate the volume of the tank. Since it has a cylindrical shape, we can use the formula for the volume of a cylinder:
V = π * r^2 * h
Where:
V = Volume
π = Pi (approximately 3.14159)
r = Radius of the base (which is half the diameter)
h = Height of the tank
Given that the diameter of the base is 5m, the radius (r) will be 5/2 = 2.5m. And the height (h) is given as 6m. Substituting these values into the formula:
V = 3.14159 * (2.5)^2 * 6
V = 3.14159 * 6.25 * 6
V = 117.8095 cubic meters
Now let's calculate the volume of oil in the tank. Since the oil level is 20cm below the brim, we need to subtract this volume from the total volume:
V_oil = V - V_air
However, we need to convert both volumes to the same unit of measurement. Since we are using meters for volume, we need to convert 20cm to meters by dividing it by 100:
V_oil = V - (0.20/100)
Substituting the values we calculated earlier:
V_oil = 117.8095 - (0.20/100)
V_oil = 117.8095 - 0.002
V_oil ≈ 117.8075 cubic meters
Now, we need to consider the thermal expansion of the crude oil. Different materials expand at different rates, and for liquids, the coefficient of thermal expansion determines how much the volume changes with temperature.
The coefficient of thermal expansion for crude oil is required to make an accurate calculation. Unfortunately, you have not provided this information. It would be best to consult a reliable source or refer to the specific composition of the crude oil to obtain the coefficient of thermal expansion.
Once you have the coefficient of thermal expansion (denoted as α), you can calculate the change in volume (ΔV) as:
ΔV = V_oil * α * ΔT
Where:
ΔV = Change in volume
V_oil = Initial volume of the oil
α = Coefficient of thermal expansion
ΔT = Change in temperature
If ΔV becomes greater than the remaining space in the tank, the oil will start to overflow.