3.1 X(eo)=2xnJe-jon where x[n] is a real sequence. Therefore X(e)=Rl∑xnlo/。 ∑xR(-mu)=∑ x[n]cos(on),and xmm)=m∑刈nm∑刈mc-m)=-2 xn] sin(oon) Since cos(on)and sin(on)are, respectively, even and odd functions of o, Xre(eJo) is an even function of o
1. C Applications of the Second Law N-Chapter6;VWB&S-8.1,8.2,8.5,8.6,8.7,8.8,9.6] 1. CI Limitations on the work that Can be supplied by a heat engine The second law enables us to make powerful and general statements concerning the maximum work that can be Q1
PaRT 1. THE SECOND LAW OF THERMODYNAMICS l.A. Background to the second Law of Thermodynamics AW 23-31(see IAW for detailed VwB&s references); VN Chapters 2, 3, 4 1-A. I Some Properties of engineering Cycles; Work and Efficiency As motivation for the development of the second law, we examine two types of processes that
1. D: Interpretation of Entropy on the Microscopic Scale- The Connection between Randomness and entropy 1. D I Entropy Change in Mixing of Two ldeal gases Consider an insulated rigid container of gas separated into two halves by a heat conducting partition so the temperature of the gas in each part is the same. One side contains air, the other side another gas, say argon, both regarded as ideal gases. The mass of gas in each side is such