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Since F is the identity for v we can replace that by p p Now we take the conjunction of this with premise 3 p & p > (s > ~t) Since x > y is equivalent to ~x v y, we can write the bracket thusly p & ~p v (s > ~t) Use the distributive law (p & ~p) v p & (s > ~t) (p & ~p) is a contradiction so we can replace it by FT dV Using the de nition of heat capacity (11) and the Maxwell relation (113), this becomes ds = cV T dT (@P @T) V dV If we now substitute (116) for (@P=@T)V, and convert dV to dˆ using dV = 1=ˆ2 dˆ, we get an expression for dq dq = Tds = cV dT P ˆ dˆ ˆ This can then be further simpli ed by noting that dˆ ˆ = (@ ln ˆ @ ln P) T dA b c d e f g h i >JK< l m n o p q r s t u v w x y z 30 likes · 1 talking about this Community Facebook is showing information to help you better

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Helping individuals and institutions improve their financial wellness through life & health insurance, retirement services, annuities and investment productsThe first truth value in the (~r∧(p→~q))→P column is T because when (~r∧(p→~q))= F and P= T, (~r∧(p→~q))→P= T The second truth value in the (~r∧(p→~q))→P column is T because when (~r∧(p→~q))= F and P= T, (~r∧(p→~q))→P= TT s Time Interval Dt = t 2 t 1 m Time Period T = 1/f s Frequency f = 1/T 1/s or Hz Velocity v = Dd/Dt m/s Velocity (wave) v = lf m/s Final Velocity (t) v f = v i at m/s Final Velocity (d) v f 2 = v i 2 2ad m/s Speed (circular) v = 2pr/T m/s Angular Speed ω = Δθ/Δt rad/s Angular Accel α = Δω/Δt rad/s 2

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C p p T = T 2 V T 2 p (b) Based on (a), show that ( C p /p) T = 0 for an ideal gas (a) Begin with the de nition of the heat capacity, C p = q dT = T dS dT, for a quasistatic process Take the derivative C p p T = T 2 S pT = T 2 S Tp (1) since S is a state function Substitute the Maxwell relation2 ~E ⊃ ~P / ~P 3 P ⊃ ~E Trans 1 (J v I) & (J v S) Dist 1 4 J v S Simp 3 5 ~J ⊃ S Imp 4 6 ~S ⊃ J Trans 5 7 ~S ⊃ S HS 2, 6 8 S v S Imp 7 9 S Taut 8 2 ~A v B Imp 1 3 (~A v B) v E Add 2 4 ~A v (B v E) Assoc 3 5 A ⊃ (B v E) Imp 4 3 ~A v ~(B ⊃ G)Eg @C P @P T = 0 for Ideal Gas V=RT/P (regardless of monatomic/diatomic etc) Graeme Ackland Lecture 9 Relationships between properties

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