How much work (in J) is required to expand the volume of a pump from 0.0 L to 2.3L against an external pressure of 1.0atm ?
work in L*atm = -p*(Vfinal-Vinitial)
Then L*atm x 101.325 = ? joules.
To calculate the work required to expand the volume of the pump, we can use the formula:
Work = -Pext * ΔV
Where:
Work is the work done (in Joules)
Pext is the external pressure (in atm)
ΔV is the change in volume (in liters)
Given:
Pext = 1.0 atm
ΔV = (2.3 L - 0.0 L) = 2.3 L
Substituting the values into the formula, we have:
Work = -1.0 atm * 2.3 L
Work = -2.3 atm L
Note: Since work is a form of energy, it is always expressed as a positive value. In this case, the negative sign indicates that work is being done on the system (the pump) by the external pressure.
Therefore, the work required to expand the volume of the pump from 0.0 L to 2.3 L against an external pressure of 1.0 atm is approximately -2.3 atm L, or simply 2.3 atm L (virtually the same value, but positive).
So, the work required is 2.3 Joules (since 1 atm L = 1 J).
To determine the work required to expand the volume of a pump, we can use the equation:
Work = Force x Distance
In this case, the force can be calculated using the definition of pressure:
Force = Pressure x Area
And the distance can be calculated using the formula:
Distance = Change in Volume
Given that the external pressure is 1.0 atm and the initial volume is 0.0 L while the final volume is 2.3 L, we can proceed with the calculations.
1. Convert the pressure from atm to Pascals (Pa):
1 atm = 101,325 Pa
Pressure = 1.0 atm = 1.0 x 101,325 Pa
2. Calculate the area of the pump:
Assuming the pump has a uniform cross-sectional area, the area can be found using a geometric formula or directly measured. Let's assume the area is A m².
3. Calculate the change in volume:
Change in Volume = Final Volume - Initial Volume
= 2.3 L - 0.0 L
= 2.3 L
4. Convert the change in volume from liters to cubic meters (m³):
1 L = 0.001 m³
Change in Volume = 2.3 L = 2.3 x 0.001 m³
5. Calculate the force:
Force = Pressure x Area
6. Calculate the distance:
Distance = Change in Volume
7. Calculate the work:
Work = Force x Distance
By following these steps and plugging in the appropriate values, you can determine the work required to expand the volume of the pump from 0.0 L to 2.3 L against an external pressure of 1.0 atm.