How Does Friction Heating Follow the First Law of Thermodynamics?

[indoguy427]

Homework Statement

I am trying to understand how the process of friction heating a block as it slides can be explained by the first law of thermodynamics.

Homework Equations

W_net(net work on object) = change in KE

change in internal energy = Q(heat added to system) - W_by (work done by system)

The Attempt at a Solution

I know that friction is doing negative work on the block. This is because the force of friction is directed opposite to the motion and thus the dot product of force and distance is negative. I can see that this is consistent with the work energy theorem because the change in KE is negative, as the block's final speed is less than its original speed. In a general sense, I understand that since energy must be conserved, this loss of KE is converted into heat energy and the block's temperature rises. However, I am having trouble understanding that from the first law.

In applying the first law I assume that since the block and floor are at the same temp, no heat is added from the floor to the block and thus Q = 0. Also, I know that W_on = -W_by.
Since the work done on the block is negative, the work done by the block is positive. That means that since change in internal energy = -W_by, the change in internal energy will be negative. This means that the block's temperature will decrease!

Can someone please help me to understand what I am doing wrong in applying the first law here? Thanks!

 

[Hootenanny]

The trick here is not to consider the block, but to consider the contact surface between the block and surface as the system.

 

[indoguy427]

hmm - if i consider the contact surface, i still don't see how it will change things...

 

[Hootenanny]

hmm - if i consider the contact surface, i still don't see how it will change things...

If one considers the contact surfaces as the system, then the frictional force is an internal force and hence the work done by friction, becomes the work done by the system.

 

[indoguy427]

hm there's a gap in my understanding with regards to the first law / internal vs. external forces... can you please explain how an internal force relates to the first law vs. an external force acting on the system?

 

[Hootenanny]

hm there's a gap in my understanding with regards to the first law / internal vs. external forces... can you please explain how an internal force relates to the first law vs. an external force acting on the system?

Simply put, the frictional force is part of the contact surface system. The frictional force is doing work against the block and since the frictional force is part of the contact surface system, then the work done by the frictional force is the work done by the contact surface system. Make sense?

 

[indoguy427]

Since the contact-surface system is doing positive work, then don't we still get a negative change in internal energy?

 

[Hootenanny]

Since the contact-surface system is doing positive work, then don't we still get a negative change in internal energy?

No, since the frictional force is in the opposite direction to the displacement the work done by the frictional force is negative (as you correctly say in your OP). Therefore, the work done by the contact surface system is negative. As per your definition of the first law this results in an increase is internal energy of the system.