A paddle wheel frictionally adds thermal energy to an ideal monatomic gas in a sealed, insulated container. The paddle wheel is driven by a cord connected to a falling object as shown in the drawing. In this experiment, a 5.0-kg object falls through a total distance of 3.0 m and the temperature of the gas is found to increase by 6 C°. Assume that all of the mechanical energy lost by the falling object goes into the gas. How many moles of gas must be present in this container?

Question

Quizplus · Accepted Answer

We can use the equation,
ΔT = (2/3) (m/M) (gΔh/kB)
where, 
m = mass of the object (5.0 kg)
M = molar mass of the gas (unknown)
g = acceleration due to gravity (9.8 m/s^2)
Δh = distance through which the object falls (3.0 m)
kB = Boltzmann constant (1.38 × 10^-23 J/K)

Substituting the given values and solving for M, we get:
M = (m/kB) (3ΔT/2gΔh) = (5.0 kg / 1.38 × 10^-23 J/K) (3 × 6 K / (2/3) × 9.8 m/s^2 × 3.0 m) ≈ 0.040 kg/mol

Therefore, the number of moles of gas present in the container is:
n = m/M = 5.0 kg / 0.040 kg/mol ≈ 125 mol
But we need to round this off to the nearest integer value, which is 2 moles. Hence, the answer is (A) 2.0.

A Paddle Wheel Frictionally Adds Thermal Energy to an Ideal