Brass is an alloy made from copper and zinc. A 0.59 kg brass sample at 96.5 C is dropped into 2.01 kg of water at 4.1 C. If the equilibrium temperature is 6.9◦C, what is the specific heat...

Brass is an alloy made from copper and zinc. A 0.59 kg brass sample at 96.5 C is dropped into 2.01 kg of water at 4.1 C. If the equilibrium temperature is 6.9◦C, what is the specific heat capacity of brass?

The specific heat of water is 4186 J/kg*C

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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Brass is an alloy made from copper and zinc. When a 0.59 kg sample made of brass at 96.5 C is dropped into 2.01 kg of water at 4.1 C, the equilibrium temperature is 6.9 C. When the brass is dropped into the water, as the temperature of brass is greater than that of water, heat flows from brass to the water. The specific heat of water is 4186 J/kg*C. To raise the temperature of 2.01 kg of water from 4.1 C to 6.9 C, the heat required is (6.9 - 4.1)*2.01*4186 J = 23558.8 J

This requires the 0.59 kg sample to cool from 96.5 C to 6.9 C. The specific heat capacity of brass is 23558.8/(0.59*(96.5 - 6.9)) = 445.65 J/kg*C

The specific heat capacity of brass is 445.65 J/kg*C

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najm1947 | Elementary School Teacher | (Level 1) Valedictorian

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Mass of Brass = 0.59 Kg

Mass of Water = 2.01 Kg

Initial Temperatur of Brass = 96.5 C

Initial Temperature of water = 4.1 C

Equilibrium temperature of Brass and Water = 6.9 C

Specific Heat of Water = 4186 J/kg C

Specific Heat of Brass  = x J/Kg C         (assume) 

Rise in Water Temperature = 6.9-4.1   = 2.8 C

Fall in Brass Temperature   = 96.5-6.9 = 89.6 C

Heat Gain/Loss = mass*Temp. Change*Specific Heat

Heat Gained by water = 2.01*2.8*4186 = 23558.81 J

Heat Lost by Brass    = 0.59*89.6*x     = 52.864*x J

Heat Loss = Heat Gain

52.864*x = 23558.81 J

x = 445.65 J/Kg

Specific Heat of Brass = 445.65 J/kg

 

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