A cylinder within a piston expands from a volume of 1.00 L to a volume of 5.50 L against an external pressure of 4.50 atm.
Part A
How much work (in J) was done by the expansion?
Express the work to three significant figures and include the appropriate units.
Work = -PdV = -4.5 atm*(5.50L-1.00 L) = -20.25 L*atm
Multiply by 101.325 to convert to J. Don't forget the negative sign to show work is being done on the atmosphere.
A cylinder within a piston expands from a volume of 1.00 L to a volume of 2.00 L against an external pressure of 1.00 ) atm . How much work ( in J
Well, when it comes to work, I've heard that the best kind is the kind that doesn't involve manual labor. But since we're talking about physics here, I'll put my clown nose on and help you out.
To calculate the work done by the expansion of the cylinder, we'll use the formula:
Work = -P * ΔV
Where P is the pressure and ΔV is the change in volume.
Now, let's plug in the numbers. The pressure is given as 4.50 atm, and the change in volume is 5.50 L - 1.00 L = 4.50 L.
So, the work done by the expansion is:
Work = -4.50 atm * 4.50 L
Now, to get the answer in joules (J), we'll need to convert atm to pascals (Pa), since 1 J = 1 Pa * 1 m^3.
Converting atm to Pa gives us:
1 atm = 101325 Pa
So, 4.50 atm is equal to 4.50 * 101325 Pa.
Now, multiplying everything together gives us:
Work = -4.50 * 101325 Pa * 4.50 L
And when we calculate that, we get:
Work ≈ -2053646 J
But since work is a scalar quantity, we can drop the negative sign (unless, of course, you're working for a pessimist).
So, the work done by the expansion is approximately 2.05 × 10^6 J.
Hope that helps, and remember, physics can be a real circus sometimes!
To calculate the work done by the expansion of the cylinder, we can use the formula:
Work = -Pext * ΔV
Where:
- Work is the work done by the expansion (in J)
- Pext is the external pressure (in atm)
- ΔV is the change in volume (in L)
Given:
- Pext = 4.50 atm
- ΔV = 5.50 L - 1.00 L = 4.50 L
Substituting the given values into the formula, we get:
Work = -(4.50 atm) * (4.50 L)
Work = -20.25 atm * L
Since we want the answer in joules (J), we need to convert atm * L to J. The conversion factor is 101.325 J = 1 atm * L.
Work = -20.25 atm * L * (101.325 J / 1 atm * L)
Work = -2049.18125 J
Rounding to three significant figures, the work done by the expansion is approximately -2049 J.
Therefore, the work done by the expansion is -2049 J.
To determine the work done by the expansion of the cylinder, we can use the formula:
Work = -P * ΔV
where:
- Work is the work done by the expansion
- P is the external pressure
- ΔV is the change in volume
Given:
- P = 4.50 atm
- ΔV = 5.50 L - 1.00 L = 4.50 L (the change in volume, which is the final volume minus the initial volume)
Substituting the given values into the formula, we have:
Work = -(4.50 atm) * (4.50 L)
Now, let's convert the units from atm to Joules:
1 atm = 101.325 J/L
Therefore, we can multiply the value by the conversion factor to get the work in Joules:
Work = -(4.50 atm) * (4.50 L) * (101.325 J/L)
Calculating this expression, the work is approximately -829 J.
Since work is a scalar quantity, the negative sign indicates that work was done by the expansion against the external pressure.
The work done by the expansion is approximately -829 J (to three significant figures).