A sphere of aluminium of 0.06 kg is placed for sufficient time in a vessel containing boiling water so that the sphere is at `100^@ C`. It is then immediately transferred to 0.12 kg copper calorimeter containing 0.30 kg of water at `25^@ C`. The temperature of water rises and attains a steady state at `28^@ C`. Calculate the specific heat capacity of aluminium. (Specific heat capacity of water, `s_w = 4.18 xx 10^3 J kg^(-1) K^(-1)`, specific heat capacity of copper `s_(Cu) = 0.387 xx 10^3 J kg^(-1) K^(-1)`)

Explanation

Given
Mass of aluminium sphere `= m_1 = 0.06 kg`
Mass of copper calorimeter `= m_2 = 0.12` kg
Mass of water in calorimeter
`=m_3 = 0.30 kg `
Specific heat capacity of copper
`=s_(cu) = s_2 = 0.387 xx 10^3 j kg^(-1) k^(-1)`
Specific heat capacity of water
`= s_w = S_3 = 4.18 xx 10^3 j kg^(-1) k^(-1)`
Initial temperature of aluminium sphere
`=T_1 = 100^@ C`
Initial temperature of calorimeter and water `=T_2 = 25^@C `
Final temperature of the mixture
`= T = 28^@ C`
We have
` s_1 = ((m_2 S_2 +m_3 s_3 )(T-T_2))/(m_1(T_1 -T))`
`=([(0.12 xx 387 )+(0.30 xx 4180 )] (28-25))/((0.006 )(100-28))`
`=((46.44 +1254 ) xx 3 )/((0.06 ) xx 72) = (3901 .32 )/(4.32)`
`= 9003.08 j kg^(-1) k^(-1)`
` therefore ` Specific heat capacity of aluminium is 903.08 J `kg^(-1) K^(-1)`