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Unformatted text preview: Some Equations for the Final Exam • Pressure vs depth h in a ﬂuid of density ρ: p = p0 + ρgh, if p0 is pressure at the surface. • Archimedes’ Principle: The magnitude of the buoyant force on an object equals the weight of the ﬂuid it displaces. • Equation of Continuity: ρAv = constant • Bernoulli’s Equation: p + 1 ρv 2 + ρgh = constant 2 • Temperature conversions for T in Kelvin: TC = T − 273.15◦ and TF = 9 TC + 32◦. 5 • Thermal expansion of solids: if α is the coeﬃcient of linear expansion, ∆L = αL∆T , ∆A = 2αA∆T , and ∆V = 3αV ∆T . • Heat capacity C = Q C Q C Q ; speciﬁc heat c = = ; molar speciﬁc heat c = = . ∆T m m∆T n n∆T • Phase changes: for solid ↔ liquid, Q = mLF for liquid ↔ gas, Q = mLV • Conductive heat ﬂow for a material with thermal conductivity k: H = −kA • Boltzmann constant: k = 1.38 × 10−23 J/K Avogadro constant: NA = 6.02 × 1023 mol−1 gas constant: R = kNA = 8.31 J/mol·K molar mass: M = NA m, if m is the mass of one molecule.
Vf ∆T . ∆x • Work by a gas: W =
Vi p dV . • For an ideal gas: pV = nRT = N kT , where n = N/NA and N is the number of molecules. Internal energy: monatomic U = 3 nRT 2 diatomic U = 5 nRT 2 polyatomic U = 3nRT Molar speciﬁc heat: monatomic CV = 3 R, CP = 5 R 2 2 diatomic CV = 5 R, CP = 7 R 2 2 polyatomic CV = 3R, CP = 4R • First Law of Thermodynamics: ∆U = Q − W , where Q is the heat into the system and W is the work done by the system. For a closed system, ∆U = 0. • Second Law of Thermodynamics: for a closed system, ∆S ≥ 0, where entropy change is f dQ given by ∆S = . T i • Eﬃciency of a heat engine: e = work performed W = ; for a Carnot engine: heat used |Qh| =1− Tc . Th ...
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- Spring '07