Gce Model Questions Vol1 2021 Physics Question 31

In two separate calorimetry experiments the same metal of unknown specific heat capacity \(c\) is used. In each experiment a calorimeter of unknown heat capacity \(C\) (J·K⁻¹) is initially at \(20^{\circ}\text{C}\). Experiment 1: \(0.300\) kg of the metal at \(120^{\circ}\text{C}\) is placed into \(0.500\) kg of water (specific heat \(c_{w}=4186\) J·kg⁻¹·K⁻¹) at \(20^{\circ}\text{C}\); the final equilibrium temperature is \(30^{\circ}\text{C}\). Experiment 2: \(0.500\) kg of the same metal at \(120^{\circ}\text{C}\) is placed into \(0.300\) kg of water at \(20^{\circ}\text{C}\); the final temperature is \(40^{\circ}\text{C}\). Assuming no heat loss to the surroundings, determine the specific heat capacity \(c\) of the metal (in J·kg⁻¹·K⁻¹) to three significant figures.