Consider nn two-state systems at temperature tt. all systems are identical, with one state at energy 0 and the other at energy ϵϵ. using the boltzmann factor for the two states, compute a formula for the energy u(t)u(t) as a function of nn,ϵϵ, and tt. using c(t)=dudtc(t)=dudt, derive a formula for the heat capacity in terms of the same variables. use the formulas for u(t)u(t) and c(t)c(t) to answer the questions below, assuming that n=6.022 × 1023 and ϵ=ϵ= 2.07 × 10-21 j for all questions.

resonant frequency

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.