How much work (in J) is required to expand the volume of a pump from 0.0 L to 2.7 L against an external pressure of 1.2 atm ?
-pdV gives work in L*atm.
Convert to Joules. 1 L*atm = 101.325 joules.
W=negative Pressure*Change in Volume W=(-P)(delta V)
To determine the work required to expand the volume of a pump, you can use the formula:
Work (W) = -Pext * ΔV
Where:
- W is the work done in joules (J)
- Pext is the external pressure in atmospheres (atm)
- ΔV is the change in volume in liters (L)
In this case, the external pressure is given as 1.2 atm, and the change in volume is from 0.0 L to 2.7 L. Therefore:
Work (W) = -1.2 atm * (2.7 L - 0.0 L)
Simplifying further:
Work (W) = -1.2 atm * 2.7 L
Work (W) = -3.24 atm·L
Since work is expressed in joules (J), we need to convert atm·L to J. The conversion factor is:
1 atm·L = 101.325 J
Therefore:
Work (W) = -3.24 atm·L * 101.325 J/atm·L
Simplifying further:
Work (W) = -328.689 J
The work required to expand the volume of the pump from 0.0 L to 2.7 L against an external pressure of 1.2 atm is approximately -328.689 J. The negative sign indicates that work is done on the system.
To calculate the work required to expand the volume of the pump against an external pressure, we can use the equation:
Work (J) = Pressure (atm) * Change in Volume (L)
First, we need to determine the change in volume. Given that the pump expands from 0.0 L to 2.7 L, the change in volume is:
Change in Volume = Final Volume - Initial Volume
Change in Volume = 2.7 L - 0.0 L
Change in Volume = 2.7 L
Next, we need to convert the pressure from atm to SI units (Pascal). Since 1 atm = 101325 Pa, we can convert 1.2 atm to Pascal:
Pressure in Pascal = 1.2 atm * 101325 Pa/atm
Pressure in Pascal = 121590 Pa
Finally, we can calculate the work using the equation:
Work (J) = Pressure (Pa) * Change in Volume (L)
Work (J) = 121590 Pa * 2.7 L
Multiplying the pressure and change in volume, we get:
Work (J) = 327993 J
Therefore, the work required to expand the volume of the pump from 0.0 L to 2.7 L against an external pressure of 1.2 atm is 327993 Joules (J).