A piston-cylinder system contains 0.1 kg of an ideal gas initially at 2 bar and 300 K. The gas undergoes a reversible expansion to a final pressure of 1 bar while the temperature remains constant. Calculate the work done by the gas during this process.
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To calculate the work done by the gas during this process, we can use the formula:
W = P * ΔV
Where:
W is the work done by the gas
P is the constant pressure during the expansion
ΔV is the change in volume of the gas
First, let's calculate the change in volume of the gas. We can use the following equation for an ideal gas:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the universal gas constant (8.314 J/(mol*K))
T is the temperature
Since the number of moles of the gas does not change, we have:
P1 * V1 = P2 * V2
Where:
P1 = 2 bar (initial pressure)
V1 is the initial volume
P2 = 1 bar (final pressure)
V2 is the final volume
We can rearrange this equation to solve for V2:
V2 = (P1 * V1) / P2
Now we can calculate the change in volume:
ΔV = V2 - V1
Substituting the values:
ΔV = [(2 bar) * (V1)] / (1 bar) - V1
ΔV = 2 * V1 - V1
ΔV = V1
Since the temperature remains constant, the relationship between pressure and volume during this process is:
P1 * V1 = P2 * V2
Substituting the values:
(2 bar) * (V1) = (1 bar) * (V2)
2 * V1 = V2
Now we can substitute the change in volume into the work equation:
W = P * ΔV
W = (1 bar) * (V1)
W = V1
Therefore, the work done by the gas during this process is equal to the initial volume of the gas, V1.
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