A styrofoam cup holds 0.30Kg of water at a temperature of 22^circ C . If 0.05Kg of ice is added, a. Calculate the change in temperature of the water produced by the melting ice b. What is the final temperature of the contents of the cup? (Assume the mass and specific heat capacity of Styrofoam is negligible)

To solve this problem, we need to use the principles of heat transfer and the specific heat capacities of water and ice.<br /><br />Given information:<br />- The Styrofoam cup holds 0.30 kg of water at a temperature of 22°C.<br />- 0.05 kg of ice is added to the cup.<br /><br />a. Calculate the change in temperature of the water produced by the melting ice:<br /><br />Let's assume the final temperature of the contents of the cup is T_f.<br /><br />The heat lost by the water as it cools down to the final temperature T_f is equal to the heat gained by the ice as it melts.<br /><br />The heat lost by the water can be calculated using the formula:<br /><br />Q_water = m_water * c_water * (T_initial - T_f)<br /><br />Where:<br />- Q_water is the heat lost by the water<br />- m_water is the mass of the water (0.30 kg)<br />- c_water is the specific heat capacity of water (4.18 J/g°C)<br />- T_initial is the initial temperature of the water (22°C)<br />- T_f is the final temperature of the contents of the cup<br /><br />The heat gained by the ice as it melts can be calculated using the formula:<br /><br />Q_ice = m_ice * L_f<br /><br />Where:<br />- Q_ice is the heat gained by the ice<br />- m_ice is the mass of the ice (0.05 kg)<br />- L_f is the latent heat of fusion of ice (334 J/g)<br /><br />Since the heat lost by the water is equal to the heat gained by the ice, we can set up the equation:<br /><br />Q_water = Q_ice<br /><br />m_water * c_water * (T_initial - T_f) = m_ice * L_f<br /><br />0.30 kg * 4.18 J/g°C * (22°C - T_f) = 0.05 kg * 334 J/g<br /><br />Solving this equation will give us the final temperature T_f.<br /><br />b. What is the final temperature of the contents of the cup?<br /><br />Once we have calculated the final temperature T_f in part (a), we can conclude that the final temperature of the contents of the cup is T_f.<br /><br />Note: The specific heat capacity of Styrofoam is negligible, so we can ignore its contribution to the heat transfer.