Calculate the heat gained by the calorimeter and water, and the energy lost by the metal nut.

Here's the solution to the problem: b) i) Heat gained by the calorimeter and water. Step 1: Calculate the temperature change. The initial temperature of the calorimeter and water is 22.0°C, and the final temperature is 52°C. T = 52°C - 22.0°C = 30°C Step 2: Calculate the heat gained by the copper calorimeter. Mass of copper calorimeter, m_c = 0.8 kg Specific heat capacity of copper, c_c = 400 Jkg^-1K^-1 Q_c = m_c c_c T Q_c = 0.8 kg × 400 Jkg^-1K^-1 × 30 K Q_c = 9600 J Step 3: Calculate the heat gained by the water. Mass of water, m_w = 0.6 kg Specific heat capacity of water, c_w = 4200 Jkg^-1K^-1 Q_w = m_w c_w T Q_w = 0.6 kg × 4200 Jkg^-1K^-1 × 30 K Q_w = 75600 J Step 4: Calculate the total heat gained by the calorimeter and water. Q_total = Q_c + Q_w Q_total = 9600 J + 75600 J Q_total = 85200 J b) ii) Energy supplied (lost) by the metal nut. According to the principle of calorimetry, the heat lost by the hot object (metal nut) is equal to the heat gained by the cold objects (calorimeter and water), assuming no heat loss to the surroundings. Q_nut\_lost = Q_total Q_nut\_lost = 85200 J b) iii) The specific heat capacity of the material making the nut. Step 1: Identify the given values for the nut. Mass of metal nut, m_nut = 0.4 kg Initial temperature of nut, T_nut\_initial = 300°C Final temperature of nut, T_nut\_final = 52°C Heat lost by nut, Q_nut\_lost = 85200 J (from part ii) Step 2: Calculate the temperature change of the nut. T_nut = T_nut\_initial - T_nut\_final T_nut = 300°C - 52°C = 248°C Step 3: Use the formula for heat lost to find the specific heat capacity (c_nut). Q_nut\_lost = m_nut c_nut T_nut 85200 J = 0.4 kg × c_nut × 248 K c_nut = 85200 J0.4 kg × 248 K c_nut = (85200)/(99.2) Jkg^-1K^-1 c_nut ≈ 858.87 Jkg^-1K^-1 c) Calculate the specific latent heat of fusion of ice. Step 1: Calculate the energy supplied by the electric heater. Power of heater, P = 60 W Time, t = 112 s E = P × t E = 60 W × 112 s E = 6720 J Step 2: Use the formula for latent heat to find the specific latent heat of fusion (L_f). Mass of ice, m_ice = 20 g = 0.020 kg The energy supplied by the heater is used to melt the ice. E = m_ice L_f 6720 J = 0.020 kg × L_f L_f = 6720 J0.020 kg L_f = 336000 Jkg^-1 That's all for today. Send me the next one 📸