A simple thermodynamic question

[arkofnoah]

Homework Statement

When a sealed Thermos bottle of hot coffee is shaken, what changes, if any, takes place in the temperature of the coffee and its internal energy? Justify your answer.

Homework Equations

Internal energy = random kinetic energy + random potential energy

The Attempt at a Solution

The answer given says that because work is done on the system there is an increase in internal energy. But isn't the work done used to increase the mechanical energy of the system, not the internal energy. There should be no increase in the temperature, shouldn't it?

 

[Red_CCF]

Homework Statement

When a sealed Thermos bottle of hot coffee is shaken, what changes, if any, takes place in the temperature of the coffee and its internal energy? Justify your answer.

Homework Equations

Internal energy = random kinetic energy + random potential energy

The Attempt at a Solution

The answer given says that because work is done on the system there is an increase in internal energy. But isn't the work done used to increase the mechanical energy of the system, not the internal energy. There should be no increase in the temperature, shouldn't it?

Logically I would think that by shaking the bottle the particles kinetic energy increases (they move faster due to the shaking) thus increasing temperature?

 

[arkofnoah]

but if i remember correctly the internal energy of a system excludes the energies due to the state of the body as a whole such as the (translational) kinetic energy due to the motion of the body and the (gravitational) potential energy due to the height of the body. Internal energy includes only 'random' energy, doesn't it?

 

[Mapes]

But isn't the work done used to increase the mechanical energy of the system, not the internal energy. There should be no increase in the temperature, shouldn't it?

After the thermos and the coffee inside have stopped moving, the mechanical energy is the same as what it was originally. Friction has converted the additional mechanical energy into thermal energy (internal energy).

 

[rwisz]

I would like to provide a more thorough explanation to this question. Firstly, it is important to understand that temperature is a measure of the average kinetic energy of the particles in a system. When the sealed Thermos bottle of hot coffee is shaken, the kinetic energy of the particles in the coffee increases due to the shaking motion. This increase in kinetic energy leads to an increase in temperature.

However, it is also important to consider the internal energy of the system. Internal energy is the sum of the random kinetic energy and potential energy of the particles in a system. When the coffee is shaken, the particles gain kinetic energy, but they also collide with each other and the walls of the Thermos bottle, leading to an increase in potential energy. This increase in potential energy also contributes to the overall increase in internal energy of the system.

Furthermore, the work done on the system during shaking also contributes to the increase in internal energy. This work is not just used to increase the mechanical energy of the system, but it also leads to an increase in the potential energy of the particles as they move against each other and the walls of the Thermos bottle.

In summary, when a sealed Thermos bottle of hot coffee is shaken, both the temperature and internal energy of the coffee increase due to the increase in kinetic energy, potential energy, and work done on the system. This is in accordance with the first law of thermodynamics, which states that energy cannot be created or destroyed, but can only be transferred from one form to another.