A horizontally-oriented cylinder contains and unknown noble gas at 48400 Pa and is sealed with a circular massless piston or radius 26.1 cm. The piston is isobarically moved inward 18.9 cm, and 18600 J of heat is removed from the gas during this process. Determine the internal energy change of the gas.
To determine the internal energy change of the gas, we can use the First Law of Thermodynamics, which states:
ΔU = Q - W
Where:
ΔU = Internal energy change of the gas
Q = Heat added or removed from the system
W = Work done on or by the system
Since the process is isobaric, the work done on the gas is given by:
W = PΔV
Where:
P = Pressure of the gas
ΔV = Change in volume
First, we need to calculate the initial volume of the gas before the piston is moved inward:
V_initial = πr^2 * h
V_initial = π * (0.261 m)^2 * h
V_initial = 0.05325144 * h
Where h is the height of the cylinder and πr^2 is the area of the piston.
Since the radius of the piston is 26.1 cm = 0.261 m, the initial volume of the gas is V_initial = 0.05325144 * h
When the piston is moved inward 18.9 cm = 0.189 m, the final volume of the gas becomes:
V_final = πr^2 * (h - 0.189)
V_final = π * (0.261)^2 * (h - 0.189)
V_final = 0.05325144 * (h - 0.189)
The change in volume is then:
ΔV = V_final - V_initial
ΔV = 0.05325144 * (h - 0.189) - 0.05325144 * h
Now, we can calculate the work done on the gas:
W = PΔV
W = 48400 Pa * ΔV
Next, we can substitute the given values into the equation for internal energy change:
ΔU = Q - W
ΔU = -18600 J - 48400 Pa * ΔV
Finally, we can calculate the internal energy change of the gas by plugging in the values for ΔV and solving the equation.