Consider N two-state systems at temperature T. All systems are identical, with one state at energy 0 and the other at energy ϵ.
Using the Boltzmann factor for the two states, compute a formula for the energy U(T) as a function of N,ϵ, and T.
Using C(T)=dU/dT, derive a formula for the heat capacity in terms of the same variables.
Use the formulas for U(T) and C(T) to answer the questions below, assuming that N=6.022 × 1023 and ϵ= 2.07 × 10-21 J for all questions:
1) Compute the internal energy U when T-200 K.
2) Compute the heat capacity when T-200 K.
3) Compute the heat capacity when T-250 K.
4) Compute the heat capacity when T-20 K.

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

Researchers determine that the biodiversity in a woodland region is declining. they identify two major threats to the region's biodiversity, a method to address each threat, and the expected outcome of each method. this information is shown in the table. a) reforestation would not benefit many species because most forest species live on the ground. b) reforestation would take the longest time to be effective because trees take several years to grow. c) biological augmentation would benefit only a few species because is is typically not very effective. d) biological augmentation would take less time to ve effective because it targets the majority of prey species.

Suppose you increase your walking speed from 7 m/s to 13 m/s in a period of 2 s. what is your acceleration?