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**1. 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.

**2. 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)

**3. 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!