Question

A copper calorimeter weighing 57.5 g contains 60 g of water at 12°C. 55 g of iron nails at 100°C are dropped into the calorimeter ands stirred rapidly. The final temperature attained by the calorimeter and its contents is 20°C. Calculate the specific heat of iron. (Sp. heat of copper = 0.4 J/g°C, Sp. heat of water = 4.2 J/g°C).

Answer 1

Mass of calorimeter, m₁ = 57.5 g

Specific heat capacity of calorimeter, C₁ = 0.4 J/g°C

Mass of water taken, m₂ = 60g

Specific heat capacity of water, C_z = 4.2 J/g°C

Mass of iron nails, m₂ = 55g

Specific heat capacity of iron = C₃

Initial temperature of iron nails, x = 100°C

Initial temperature of calorimeter + water, y = 12°C 

Final temperature of the mixture, z = 20°C

Heat lost by iron nails = heat gained by calorimeter and water

m₃C₃ (x - z) = m₁C₁(z - y) + m₂C₂(z - y)

`"C"_3 = (("m"_1"C"_1 + "m"_2"C"_2)("z" - "y"))/("m"_3( "x" - "z")`

= `((57.5 xx 0.4 + 60 xx 4.2)(20 - 12))/(55 xx ( 100 - 20))` = 0.5 J/g°C