An aluminum calorimeter with a mass of 100 g contains 250 g of water. The calorimeter and water are in thermal equilibrium at 10.0°C. Two metallic blocks are placed into the water. One is a 75.0-g piece of copper at 60.0°C. The other has a mass of 70.0 g and is originally at a temperature of 100°C. The entire system stabilizes at a final temperature of 20.0°C.

Determine the specific heat of the unknown sample.

The specific heat of the unknown sample is 1822.14 J/kg.k

Explanation:

Given;

mass of aluminum calorimeter, = 100 g

mass of water, = 250 g

stabilizing temperature of water-calorimeter, ΔT =  10.0°C

mass of copper, = 75 g

initial temperature of copper, =  60.0°C

mass of unknown sample, = 70.0 g

initial temperature of unknown sample, =  100°C.

The final temperature of the entire system, t = 20.0°C

Apply the principle of conservation of energy;

energy used to heat water and calorimeter is equal to energy released by copper and unknown sample.

where;

Q is energy used to heat water and calorimeter

is the specific heat capacity of copper

is the specific heat capacity of unknown sample

Make subject of the formula;

Therefore, the specific heat of the unknown sample is 1822.14 J/kg.k