A vertical cylinder,closed at the bottom end,contains 0.0100 mol of ideal gas.It is fitted at the top with a piston that 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? (R = 8.31 J/mol ∙ K)
A)290 K
B)413 K
C)3620 K
D)405 K
E)500 K

Question

Quizplus · Accepted Answer

Using the equation for ideal gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature.

Since the piston can move freely, the pressure of the gas is equal to the atmospheric pressure. We can assume that the atmospheric pressure is 1 atm.

Initially, the volume of the gas is equal to the volume of the cylinder:

V = πr^2h = π(0.25)^2(0.25) = 0.0491 m^3

The mass of the piston is not needed for this calculation.

The number of moles of gas is given as 0.0100 mol.

Substituting all the known values in the ideal gas law equation, we get:

P(0.0491) = (0.0100)(8.31)T

1(0.0491) = (0.0100)(8.31)T

T = 595.91 K

However, this temperature is the absolute temperature in Kelvin. To convert it to Celsius, we subtract 273.15:

T = 322.76°C

Therefore, the answer is B) 413 K.

A Vertical Cylinder,closed at the Bottom End,contains 0