1 kg aluminum dumbbell initially held 2 meters above the floor is allowed to fall. This experiment is performed inside a room whose dimensions are 10m × 5m × 3m. Assuming that the walls of the room do not conduct heat and that the room is empty (no other objects are presentesides the dumbbell itself), estimate the change of the temperature inside the room as a result as a result of dropping the dumbbell. Thermodynamic properties of Aluminum and air can be looked up.

Question

1 kg aluminum dumbbell initially held 2 meters above the floor is allowed to fall. This experiment is performed inside a room whose dimensions are 10m × 5m × 3m. Assuming that the walls of the room do not conduct heat and that the room is empty (no other objects are presentesides the dumbbell itself), estimate the change of the temperature inside the room as a result as a result of dropping the dumbbell. Thermodynamic properties of Aluminum and air can be looked up.

Answer 1

i think i figured it out

Answer 2

To estimate the change in temperature inside the room as a result of dropping the aluminum dumbbell, we can consider the process in which the potential energy of the dumbbell is converted into heat energy.

Here's a step-by-step approach to finding the answer:

1. Calculate the potential energy of the dumbbell before it falls:
Potential Energy (PE) = mass x gravitational acceleration x height
Given: mass = 1 kg, height = 2 m, and gravitational acceleration = 9.8 m/s^2

PE = 1 kg x 9.8 m/s^2 x 2 m = 19.6 J

2. Assume that all the potential energy is converted into heat energy and transferred to the room. We can calculate the amount of heat energy produced using the specific heat capacity and the mass of the room.

First, we need to determine the mass of the room. To do this, we need to calculate the volume of the room:
Volume = length x width x height
Given: length = 10 m, width = 5 m, and height = 3 m

Volume = 10 m x 5 m x 3 m = 150 m^3

Since we know the density of air is approximately 1.225 kg/m^3, we can calculate the mass of the room:
Mass = density x volume
Mass = 1.225 kg/m^3 x 150 m^3 = 183.75 kg

3. Now, we can calculate the change in temperature (ΔT) of the room using the heat capacity equation:

Heat energy = mass x specific heat capacity x ΔT

Rearranging the equation, we can find:

ΔT = Heat energy / (mass x specific heat capacity)

The specific heat capacity of aluminum is 896 J/kg·K, and the specific heat capacity of air is around 1005 J/kg·K.

ΔT = 19.6 J / (183.75 kg x 1005 J/kg·K) ≈ 0.000106 K

Therefore, the estimated change in temperature inside the room as a result of dropping the aluminum dumbbell is approximately 0.000106 Kelvin, which is a negligible change and within experimental error.