Question

What is the total translational kinetic energy of the air molecules in a room of volume 23 m³ if the pressure is 9.5 × 10⁴ Pa (the room is at fairly high elevation) and the temperature is 21°C? Is any item of data unnecessary for the solution?

a) 5.28 × 10² J, No
b) 7.46 × 10² J, No
c) 9.81 × 10² J, Yes
d) 11.50 × 10² J, Yes

Answer 1

The total translational kinetic energy of the air molecules in the room can be calculated using the temperature alone. The correct answer is 9.81 x 10² J.

Step-by-step explanation:

The total translational kinetic energy of the air molecules in the room can be calculated using the temperature alone. The equation for translational kinetic energy is KE = 3/2kT, where k is Boltzmann's constant and T is the temperature in Kelvin. Substituting the given temperature of 21°C into the equation gives:

KE = (3/2)(1.38 x 10-23 J/K)(294 K) = 9.81 x 102 J

Therefore, the correct answer is c) 9.81 x 102 J.