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?
A) 290 K
B) 413 K
C) 3620 K
D) 405 K
E) 500 K

Question

Quizplus · Accepted Answer

We can use the ideal gas law to solve for the temperature:
PV = nRT
We know the volume of the cylinder and the number of moles of gas, so we need to solve for the pressure. The pressure is equal to the weight of the piston divided by its surface area. The surface area can be found using the radius of the cylinder and the height of the piston:
A = πr^2 = π(0.25m)^2 = 0.196 m^2
The weight of the piston is:
W = mg = 14.0 kg x 9.8 m/s^2 = 137.2 N
So the pressure is:
P = W/A = 137.2 N / 0.196 m^2 = 700.0 Pa
Now we can solve for the temperature:
T = PV/nR = (700.0 Pa)(0.10 m^3) / (0.0100 mol)(8.31 J/mol*K) = 413 K
Therefore, the answer is B.

A Vertical Cylindrical Cylinder, Closed at the Bottom End, Contains