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Answer :
Final answer:
To calculate the work when a system contracts from 1.55 L to 0.85 L at a constant pressure of 99.8 kPa, convert the pressure to Pa and the volume to m³, then use the pressure-volume work formula. The result is -69.86 J, which indicates the system had 69.86 J of work done on it.
Explanation:
To calculate the work done during the contraction of a system's volume from 1.55 to 0.85 L under a constant pressure of 99.8 kPa, one needs to use the formula for pressure-volume work:
W = P ΔV
Where:
- W is the work in joules (J).
- P is the constant pressure in kilopascals (kPa), which needs to be converted into pascals (Pa) where 1 kPa = 1000 Pa.
- ΔV is the change in volume in liters, which needs to be converted into cubic meters where 1 L = 0.001 m³.
First, convert the pressure from kPa to Pa:
P = 99.8 kPa × 1000 Pa/kPa = 99800 Pa
Next, calculate the change in volume in cubic meters:
ΔV = (0.85 L - 1.55 L) × 0.001 m³/L = -0.0007 m³
(Note that the change in volume is negative because the volume contracts.)
Now, calculate the work:
W = 99800 Pa × -0.0007 m³ = -69.86 J
Since the work is done by the system (contraction), it is considered positive work by the system. However, if the system contracts against an external pressure, it is conventionally negative work done on the system. Therefore, 69.86 J of work were done on the system.
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