Two systems with heat capacities C 1 and C 2 , respectively, interact thermally and come to a common temperature T f . If the initial temperature of system 1 was T 1 , what was the initial temperature of system 2? You may assume that the total energy of the combined systems remains constant.
Text Solution
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Sol. We assume that the initial temperature of system 2 is T 2 . According to the conservation of energy, we know the heat released from system 1 is equal to that absorbed by the other system i.e.,
C 1 (T f – T 1 ) = C 2 (T 2 – T f ).
The solution is
T 2 = 
(T f – T 1 ) +T f .
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