Final answer:
The equilibrium temperature is found by equating the heat lost by 17 kg of water cooling down from 20 degrees Celsius to the heat gained by 3 kg of ice melting and warming up to the final temperature in an insulated system.
Step-by-step explanation:
To find the equilibrium temperature when 3 kg of ice at 0 degrees Celsius is added to 17 liters (which is equivalent to 17 kg as the density of water is 1 kg/L) of water at an initial temp of 20 degrees Celsius in a fully insulated tank, we equate the heat lost by the water to the heat gained by the ice.
The heat lost by the water can be calculated by Q_water = m_water * c_water * (T_final - T_initial_water), where m_water is the mass of the water (17 kg), c_water is the specific heat capacity of water (4.18 J/g°C), and T_final is the final temperature we are looking for.
The heat gained by the ice consists of two parts: the heat required to melt the ice and the heat required to raise the temperature of the resulting water from 0 °C to the final temperature. This can be articulated as Q_ice = m_ice * L_f + m_ice * c_water * (T_final - T_initial_ice), where m_ice is the mass of the ice (3000 g), L_f is the latent heat of fusion for ice (334 J/g), and T_initial_ice is 0 °C.
Set these two equations equal and solve for T_final, keeping in mind to convert masses to grams when necessary since the specific heat capacity and latent heat are given per gram. We ignore the heat absorbed or transferred by the tank as stated in the question, so no additional heat transfer occurs to the surroundings.