A vertical cylindrical cylinder, closed at the bottom end, contains 0.0100 moles of gas. It is fitted at
the top with a piston, which can move freely. The mass of the piston is 14.0 kg and the initial height of
the piston above the bottom of the cylinder is 25 cm. What is the temperature of the gas?
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To find the temperature of the gas, we can use the ideal gas law equation, which is:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas
In this case, the initial pressure and volume of the gas are not given. However, since the piston is at the top and can move freely, we can assume that the pressure remains constant throughout the process.
To find the volume of the gas, we need to calculate the final height of the piston. We can do this by setting up an equation involving the mass of the piston, the acceleration due to gravity, and the initial and final heights:
mgΔh = 0.0100 moles * R * ΔT
Where:
m is the mass of the piston
g is the acceleration due to gravity
Δh is the change in height of the piston (initial height - final height)
R is the universal gas constant
ΔT is the change in temperature
In this case, the mass of the piston is given as 14.0 kg, the initial height is 25 cm, and the change in height is not given.
Solving this equation will give us the change in height of the piston, which we can use to calculate the final volume of the gas.
Once we have the volume and the number of moles of the gas, we can rearrange the ideal gas law equation to solve for the temperature:
T = PV / (nR)
Substituting the values for pressure, volume, number of moles, and the ideal gas constant will give us the temperature of the gas.
Keep in mind that this method assumes the gas behaves ideally and that there are no other factors, such as heat transfer, that would affect the temperature.