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.
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.
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