A gas expands from 282 mL to 971 mL at constant temperature.Calculate the work done (in joules) by the gas if it expands against a constant pressure of 6.00 atm.
To calculate the work done by the gas, we can use the equation:
Work (W) = -PΔV
Where:
- P is the pressure
- ΔV is the change in volume
Given:
- The initial volume (V1) is 282 mL
- The final volume (V2) is 971 mL
- The pressure (P) is 6.00 atm
First, we need to convert the volumes from milliliters (mL) to liters (L) since pressure is given in atmospheres (atm).
V1 = 282 mL = 0.282 L
V2 = 971 mL = 0.971 L
Now, we can calculate the change in volume (ΔV):
ΔV = V2 - V1 = 0.971 L - 0.282 L
ΔV = 0.689 L
Finally, we can calculate the work done by the gas:
W = -PΔV = -(6.00 atm) x (0.689 L)
W = -4.13 atm L
However, the unit of work is Joules (J), not atm L. To convert from atm L to Joules, we can use the conversion factor:
1 atm L = 101.3 J (approximately)
W = -4.13 atm L x (101.3 J / 1 atm L)
W = -418.669 J (rounded to three significant figures)
Therefore, the work done by the gas is approximately -418.669 Joules. The negative sign indicates that work is done on the gas, which means energy is absorbed by the system.