At standard atmospheric pressure,at what temperature is the total kinetic energy of a bottle containing 0.15 mol of neon equal to that of a major league pitcher's fastball (0.145 kg ball travelling at 95 mph)?

Question

Quizplus · Accepted Answer

The total kinetic energy of the 0.145 kg baseball travelling at 95 mph can be calculated as:
KE = 0.5mv^2 
KE = 0.5(0.145 kg)(42.267 m/s)^2 
KE = 134.2 J

We can equate this to the total kinetic energy of the 0.15 mol of neon in the bottle, which can be calculated using the equation:
KE = (3/2)NkT 
where N is the number of particles (in this case, 0.15 mol of neon), k is the Boltzmann constant (1.38 x 10^-23 J/K), and T is the temperature in Kelvin.

Substituting in the values, we get:
134.2 J = (3/2)(0.15 mol)(6.022 x 10^23 particles/mol)(1.38 x 10^-23 J/K)T 
T = 70 K

Therefore, the answer is B) 70 K.

At Standard Atmospheric Pressure,at What Temperature Is the Total Kinetic