Glass of water has mass of 240g at room temp (25°C). Add 50g of 0°C ice. What final temp after ice is melted. (at equilibrium).
To determine the final temperature after the ice has melted and reached equilibrium, you need to consider the principles of heat transfer and the concept of thermal equilibrium.
The first step is to calculate the heat gained or lost by each component involved.
1. Calculate the heat gained or lost by the glass of water (initially at 25°C):
The specific heat capacity of water is approximately 4.18 J/g°C. Thus, the heat gained or lost by the glass of water (Q1) can be calculated using the formula:
Q1 = mass1 * specific heat capacity1 * (final temperature - initial temperature)
Q1 = 240g * 4.18 J/g°C * (final temperature - 25°C)
2. Calculate the heat gained or lost by the ice (initially at 0°C):
The heat gained or lost by the ice (Q2) can be calculated using the formula:
Q2 = mass2 * specific heat capacity2 * (final temperature - initial temperature)
Q2 = 50g * 2.09 J/g°C * (final temperature - 0°C)
(The specific heat capacity of ice is approximately 2.09 J/g°C)
3. As the ice melts, it absorbs heat from the water until both reach the same temperature at equilibrium. At this point, we can consider that the heat gained by the ice is equal to the heat lost by the water:
Q1 = Q2
By setting Q1 equal to Q2, we can solve for the final temperature:
240g * 4.18 J/g°C * (final temperature - 25°C) = 50g * 2.09 J/g°C * (final temperature - 0°C)
Simplifying the equation:
996.96 * (final temperature - 25) = 104.5 * final temperature
Now, solve for the final temperature:
996.96 * final temperature - 24,924 = 104.5 * final temperature
892.46 * final temperature = 24,924
final temperature ≈ 27.92°C
So, the final temperature after the ice is completely melted and thermal equilibrium is reached is approximately 27.92°C.