calculate the work done on the system when 1.00mol of gas held behind a piston expands irreversibly from a volume of 1.00dm cube to a volume of 10.0dm cube against an external pressure of 1.00 bar
To calculate the work done on the system during an irreversible expansion, we can use the formula:
W = -Pext * ΔV,
where W is the work done, Pext is the external pressure, and ΔV is the change in volume.
Given:
Number of moles (n) = 1.00 mol
Initial volume (V1) = 1.00 dm³
Final volume (V2) = 10.0 dm³
External pressure (Pext) = 1.00 bar
First, we need to convert the external pressure from bar to Pascal (Pa) because the units of the gas constant are in J/mol·K:
1 bar = 100,000 Pa
So, Pext = 1.00 bar * 100,000 Pa/bar = 100,000 Pa.
Next, we need to convert the volumes from dm³ to m³ because the SI unit of volume is cubic meters:
V1 = 1.00 dm³ * (1/1,000 m³/dm³) = 0.001 m³
V2 = 10.0 dm³ * (1/1,000 m³/dm³) = 0.01 m³
Now we can calculate the change in volume:
ΔV = V2 - V1 = 0.01 m³ - 0.001 m³ = 0.009 m³
Finally, we can calculate the work done on the system using the formula:
W = -Pext * ΔV = -100,000 Pa * 0.009 m³ = -900 J
Therefore, the work done on the system during the irreversible expansion is -900 Joules. The negative sign indicates work done by the system on the surroundings due to expansion.