Question

A cup contains 185 g of coffee at 99.4 °C. Suppose 62.7 g of ice is added to the coffee. What is the temperature of the coffee after all of the ice melts? The enthalpy of fusion of water can be found in this table. Assume the specific heat capacity of the coffee is the same as water.

final=°C

Answer 1

The final temperature of the coffee after all of the ice melts is approximately 7.3°C.

Step-by-step explanation:

To find the temperature of the coffee after all of the ice melts, we can use the principle of conservation of energy. The heat lost by the coffee when it cools down is equal to the heat gained by the ice when it melts. We can use the equation Q1 = Q2 to solve for the final temperature. The equation can be written as m1c1(T1 - final temperature) = m2c2( final temperature- T2), where m1 and m2 are the masses of the coffee and ice, c1 and c2 are the specific heat capacities of the coffee and ice, T1 and T2 are the initial temperatures of the coffee and ice..

Plugging in the given values, we have 185g * c1 * (99.4°C - final temperature) = 62.7g * 2.062 J/(g•°C) * ( final temperature - 0°C). Solving for the final temperature, we find that the final temperature ≈ 7.3°C. Therefore, the temperature of the coffee after all of the ice melts is approximately 7.3°C.