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热力学
12
engines
Rankine cycle
Rankine cycle
锅炉/汽轮机/凝汽器/泵 · η=1−qout/qin · T-s图
Ideal steam power cycle · η = w_net / q_in = 1 − q_out / q_in
Brayton cycle
Brayton cycle
燃气轮机 · η=1−1/rp^((γ−1)/γ) · 压比rp
Ideal gas-turbine cycle · η = 1 − 1 / rp^((γ−1)/γ)
Diesel cycle
Diesel cycle
η=1−(1/r^(γ−1))·[(α^γ−1)/(γ(α−1))] · 压缩比/预胀比
Ideal compression-ignition cycle · η = 1 − (1/r^(γ−1))·(α^γ−1)/(γ(α−1))
Vapor-compression refrigeration cycle
Vapor-compression refrigeration cycle
蒸汽压缩 · COP_R=QL/Wnet ≤ TL/(TH−TL) Carnot
COP_R = QL / Wnet ≤ TL / (TH − TL) (Carnot bound)
Heat pump — coefficient of performance
Heat pump — coefficient of performance
COP_HP=TH/(TH−TL)=COP_R+1 · vs电阻加热COP=1
COP_HP = QH / Wnet ≤ TH / (TH − TL) = COP_R + 1
Ideal Stirling cycle
Ideal Stirling cycle
2等温+2等容+回热器 · 理想回热η=1−TL/TH
2 isothermals + 2 isochorics + a regenerator ⇒ η = 1 − TL/TH (Carnot)
P–V diagram · the four basic processes
P–V diagram · the four basic processes
等压/等容/等温/绝热 · W=∫P dV · 面积=功
isobaric · isochoric · isothermal · adiabatic — work is the area under the path W = ∫P dV
Isothermal vs adiabatic expansion
Isothermal vs adiabatic expansion
等温PV=const vs 绝热PV^γ=const · 绝热更陡
same start, two paths — the adiabat is steeper, so it does less work and cools the gas
Heating curve of water · sensible & latent heat
Heating curve of water · sensible & latent heat
加热曲线 · Q=mcΔT斜段+Q=mL平台 · 冰→水→汽
temperature climbs while heating one phase (Q = mcΔT), and stays flat while it changes phase (Q = mL)
Maxwell relations
Maxwell relations
U/H/F/G四势 · 混合二阶偏导相等 · 热力学方块
Equal mixed partials of U, H, F, G · ∂²Φ/∂x∂y = ∂²Φ/∂y∂x
Clausius–Clapeyron equation
Clausius–Clapeyron equation
dP/dT=L/(T·Δv) · ln(P2/P1)=−(L/R)(1/T2−1/T1)
dP/dT = L/(T·Δv) ⇒ ln(P₂/P₁) = −(L/R)(1/T₂ − 1/T₁)
Joule–Thomson effect
Joule–Thomson effect
等焓节流 · μ_JT=(∂T/∂P)_H · 反转温度以下制冷
μ_JT = (∂T/∂P)_H · cools if μ>0 (below T_inv), warms if μ<0