Carbon dioxide, as a gas, at 335 K is pumped at a very high pressure into an oil-well. If CO2 has a specific gravity of 0.367, then, calculate the gauge pressure at which CO2 is pumped.
To calculate the gauge pressure at which CO2 is pumped, we need to first understand the concept of specific gravity.
Specific gravity is the ratio of the density of a substance to the density of a reference substance. In this case, the reference substance is typically water.
The specific gravity of CO2 is given as 0.367. This means that CO2 is 0.367 times as dense as water.
Assuming the pressure unit is in pascals, we can calculate the density of CO2 at 335 K using the ideal gas law:
PV = nRT
Where:
P = Pressure (in pascals)
V = Volume (in m^3)
n = Number of moles
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature (in Kelvin)
To simplify the calculation, we can assume that the volume of CO2 is constant.
Next, we can determine the number of moles of CO2 using the specific gravity and the molar mass of CO2.
The molar mass of carbon dioxide is approximately 44.01 g/mol.
Given that the specific gravity is 0.367, it means that the density of CO2 is 0.367 times the density of water (1000 kg/m^3). Therefore, the density of CO2 can be calculated as:
density_CO2 = 0.367 * 1000 kg/m^3
Finally, we can calculate the gauge pressure using the density:
density_CO2 = moles_CO2 * molar_mass_CO2 / volume_CO2
Simplifying, we get:
P = (moles_CO2 * molar_mass_CO2 / volume_CO2) * R * T
Since the volume is constant, we can ignore it:
P = (moles_CO2 * molar_mass_CO2) * R * T
Using the relationships above, we can calculate the gauge pressure at which CO2 is pumped.
To calculate the gauge pressure at which CO2 is pumped, we need to know the density of the CO2 and the acceleration due to gravity.
Step 1: Calculate the density of CO2
Specific gravity is defined as the ratio of the density of a substance to the density of a reference substance, usually water.
Given that the specific gravity of CO2 is 0.367, we can calculate the density of CO2 relative to water.
Density of CO2 = Specific gravity of CO2 * Density of water
Density of CO2 = 0.367 * Density of water
Assuming the density of water is 1000 kg/m^3, we can calculate the density of CO2 as:
Density of CO2 = 0.367 * 1000 kg/m^3
Density of CO2 = 367 kg/m^3
Step 2: Calculate the gauge pressure
Gauge pressure is the pressure relative to atmospheric pressure. Since the question mentions pumping CO2 into an oil-well, we assume that the reference pressure is atmospheric pressure.
Gauge pressure = Absolute pressure - Atmospheric pressure
We are given the temperature (335 K) and the specific gravity of CO2 (0.367), but we still need to find the absolute pressure.
Step 3: Calculate the absolute pressure
To calculate the absolute pressure, we can use the ideal gas law, which states that:
PV = nRT
Where:
P = Pressure (in pascals)
V = Volume (in cubic meters)
n = Number of moles
R = Ideal gas constant (8.314 J/mol·K)
T = Temperature (in kelvin)
Given that CO2 is in a gas state, we assume it to behave ideally. We also assume that the volume of CO2 and the number of moles are constant.
Let's assume the volume is 1 cubic meter and the number of moles is 1.
P * 1 = 1 * 8.314 * 335
P = (8.314 * 335) pascals
P = 2772.61 pascals
Step 4: Calculate the gauge pressure
Atmospheric pressure is around 101,325 pascals.
Gauge pressure = (2772.61 - 101325) pascals
Gauge pressure ≈ -98842.39 pascals (rounded to two decimal places)
Therefore, the gauge pressure at which CO2 is pumped is approximately -98842.39 pascals.