Potential energy behind dams
Answer:
(C) 2P
Explanation:
Ideal gas law states:
PV = nRT
n (the number of moles) and R (ideal gas constant) are constant, so we can say:
(PV / T) before = (PV / T) after
Chamber X starts at pressure P, volume V, and temperature T. At equilibrium, the pressure is Px, the volume is Vx, and temperature 3T.
PV / T = Px Vx / 3T
Chamber Y starts at pressure P, volume V, and temperature T. At equilibrium, the pressure is Py, the volume is Vy, and temperature T.
PV / T = Py Vy / T
Substituting and simplifying:
Px Vx / 3T = Py Vy / T
Px Vx / 3 = Py Vy
Since the chambers are at equilibrium, Px = Py:
Vx / 3 = Vy
Vx = 3 Vy
The total volume is the same as before, so:
Vx + Vy = 2V
Substituting:
(3 Vy) + Vy = 2V
4 Vy = 2V
Vy = V / 2
Now if we substitute into our equation for chamber Y:
PV / T = Py (V/2) / T
PV = Py (V/2)
Py = 2P
The pressure in chamber Y (and chamber X) doubles at equilibrium.
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