A gas expands its volume from 4.7 L to 8.9 L at constant temperature. Answer the following:
a) If the gas expands against vacuum conditions, calculate the work (in joules) done by the gas.
b) Calculate the work done (in joules) by the gas if it expands against a constant pressure of 4.7 atm.
work = -pdV
a. If p is zero, then pdV is 0
b. substitute into the equation. dV is V2-V1.
Note that work in the above is in L*atm. You must change this to joules.
a) To calculate the work done by the gas when it expands against vacuum conditions, we can use the equation:
Work = -PΔV
Where P is the external pressure and ΔV is the change in volume. In vacuum conditions, the external pressure is zero. Therefore, the work done by the gas is:
Work = -0 × (8.9 L - 4.7 L)
= 0 J
Hence, the work done by the gas against vacuum conditions is 0 Joules.
b) To calculate the work done by the gas when it expands against a constant pressure of 4.7 atm, we can again use the equation:
Work = -PΔV
Where P is the external pressure and ΔV is the change in volume. In this case, the external pressure is 4.7 atm and the change in volume is (8.9 L - 4.7 L) = 4.2 L.
Work = -4.7 atm × 4.2 L
= -19.74 L.atm
To convert the unit of liter atmospheric (L.atm) to Joules (J), we need to use the conversion factor:
1 L.atm = 101.3 J
Work = -19.74 L.atm × 101.3 J/L.atm
= -1998.6 J
Hence, the work done by the gas when it expands against a constant pressure of 4.7 atm is approximately -1998.6 Joules.
To calculate the work done by the gas in both scenarios, we can use the formula:
Work = (Pressure)(Change in Volume)
a) If the gas expands against vacuum conditions, it means there is no external pressure acting on the gas. Therefore, the pressure is zero. The change in volume can be calculated by subtracting the initial volume from the final volume:
Change in Volume = Final Volume - Initial Volume = 8.9 L - 4.7 L = 4.2 L
Substituting these values into the formula:
Work = (0 atm) x (4.2 L) = 0 joules
Therefore, in this scenario, no work is done by the gas since there is no pressure.
b) If the gas expands against a constant pressure of 4.7 atm, we can use the given pressure value in the formula. The change in volume is the same as calculated before:
Change in Volume = 8.9 L - 4.7 L = 4.2 L
Substituting these values into the formula:
Work = (4.7 atm) x (4.2 L)
To calculate the work in joules, we need to convert the units. Since 1 atm = 101.325 J/L, we can multiply the work value by this conversion factor:
Work = (4.7 atm) x (4.2 L) x (101.325 J/L) = 201.33675 joules
Therefore, in this scenario, the work done by the gas is approximately 201.33675 joules.