A cylinder which is in a horizontal position contains an unknown noble gas at 4.63 × 104 Pa and is sealed with a massless piston. The piston is slowly, isobarically moved inward 0.202 m, while 1.95 × 104 J of heat is removed from the gas. If the piston has a radius of 0.283 m, calculate the change in internal energy of the system.
To calculate the change in internal energy of the system, we need to use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to or removed from the system, plus the work (W) done by or on the system.
Mathematically, it can be represented as:
ΔU = Q - W
In this case, we know that heat (Q) is -1.95 × 10^4 J (removed from the system), and we need to calculate the work (W) done.
Since the process is isobaric (the pressure remains constant), the work done is given by the equation:
W = P(V2 - V1)
Where:
W is the work done
P is the pressure
V2 is the final volume
V1 is the initial volume
To calculate the work, we need to find the initial and final volumes. Since the cylinder is in a horizontal position and the piston is moved inward, the volume decreases due to the change in height of the piston.
The change in volume (ΔV) can be calculated using the formula for the volume of a cylinder:
ΔV = πr^2Δh
Where:
ΔV is the change in volume
π is a mathematical constant (approximately 3.14159)
r is the radius of the piston (0.283 m)
Δh is the change in height of the piston (0.202 m)
Now we can calculate the change in internal energy (ΔU) by substituting the known values into the equation ΔU = Q - W.
ΔV = π(0.283)^2 * 0.202
ΔU = -1.95 × 10^4 - 4.63 × 10^4 * ΔV
Solving these equations will give you the change in internal energy (ΔU) of the system.
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