Final answer:
To calculate the work done by a piston with an external pressure of 12.0 atm changing the volume in the cylinder from 0.160 liters to 0.600 liters, one needs to multiply the change in volume by the pressure and take the negative of that product. This yields a value of 534.996 joules of work done by the gas.
Step-by-step explanation:
The student is asking how much work is done by a piston in joules when the volume of a cylinder changes from 0.160 liters to 0.600 liters against a constant external pressure of 12.0 atm.
To find the work done, we use the formula W = -P∆V, where W is the work done on the gas (which will be negative as the gas is doing work on the environment), P is the constant external pressure, and ∆V is the volume change.
The volume change (∆V) is Vfinal - Vinitial = 0.600 L - 0.160 L = 0.440 L.
Converting liters to cubic meters, we have 0.440 L x 10^-3 m^3/L = 4.40 x 10^-4 m^3.
The pressure must be converted to pascals, so 12.0 atm x 101325 Pa/atm = 1.2159 x 10^6 Pa.
Now calculating the work: W = - (1.2159 x 10^6 Pa) x (4.40 x 10^-4 m^3) = -534.996 J.
As the work done on the gas is negative, the gas does positive work of 534.996 J on the surroundings.