# What is the final temperature?A 23.8 g silver ring (cp = 234 J/kg·°C) is heated to a temperature of 82.2°C and then placed in a calorimeter containing 5.32 10^-2 kg of water at 24.0°C. The...

What is the final temperature?

A 23.8 g silver ring (cp = 234 J/kg·°C) is heated to a temperature of 82.2°C and then placed in a calorimeter containing 5.32 10^-2 kg of water at 24.0°C. The calorimeter is not perfectly insulated, however, and 0.144 J of energy is transferred to the surroundings before a final temperature is reached.

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### 1 Answer

A 23.8 g silver ring (cp = 234 J/kg*C) is heated to a temperature of 82.2 C and then placed in a calorimeter containing 5.32*10^-2 kg of water at 24.0 C. The calorimeter is not perfectly insulated and 0.144 J of energy is transferred to the surroundings before a final temperature is reached. The final temperature has to be determined.

Let the final temperature be T. The silver ring is cooled from 82.2 C to T C. The heat given off during this process is 23.8*10^-3*234*(82.2 - T) A part of this heat, 0.144 J escapes. The rest is used to raise the temperature of water from 24 C to T.

=> 23.8*10^-3*234*(82.2 - T) = 5.32*10^-2*4181*(T - 24) + 0.144

=> 457.8 - 5.569T = 222.42T - 5338.3 + 0.144

=> 227.98T = 5795.9

=> T = 25.42 C

The final temperature is 25.42 C