L13 - ReviewMideTerm - PH2103 Thermal Physics Lecture 13...

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PH2103 Thermal Physics Lecture 13: Review of Mid Term Exam Massimo Pia Ciamarra [email protected] SPMS-PAP-03-14 Discussion Forum
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Ex 1 Two bodies of the same substance, both of mass m , having temperature T 1 and T 2 , are placed in thermal contact. In the temperature interval (T 1 ,T 2 ), the specific heat of the bodies varies according to the law c(T) = a +bT . Determine the equilibrium temperature of the bodies, assuming that no heat is exchanged with the outside. a = 0.5 kcal/(kg º C); b = 10 -3 kcal/(kg º C 2 ); T 1 = 0 º C; T 2 = 100 º C;
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Ex 1 ..assuming that no heat is exchanged with the outside. This means that energy of the combined system is conserved. We know that the temperatures of the two object change as these exchange heat. If Q 1 and Q 2 are the heat flowing into object 1 and 2, respectively, the conservation of energy tells us Q 1 = -Q 2 . The specific heat is defined as Accordingly, we have and c = 1 m dQ dT dQ = m dT Q 1 = m T 1 T eq c ( T ) dT Q 2 = m T 2 T eq c ( T ) dT
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Ex 1 We find Q 1 = T 1 T eq c ( T ) dT = T 1 T eq a + bT dT = aT + 1 2 bT 2 | T 1 T eq = a ( T eq T 1 )+ 1 2 b ( T eq 2 T 1 2 ) Q 2 = T 2 T
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