1. Assume that 10 g of steam is added to 100 g of water initially at 19°C. The water is inside an aluminum cup of mass 35 g. The cup is inside a perfectly insulating calorimetric container that prevents heat flow from the outside environment. Find the final temperature of the water after equilibrium is reached.
Specific heat of water: 4.19 kJ/(kg × K)
Specific heat of aluminum: 922 J/(kg ×
K)
Latent heat of fusion for water: 334 kJ/kg
Latent heat of vaporization for water: 2260 kJ/kg
To find the final temperature of the water after equilibrium is reached, we need to consider two processes: the heat gained by the water and the heat lost by the steam.
Let's break down the steps to find the final temperature:
1. Determine the heat gained by the water:
- The initial temperature of the water is 19°C, and assuming it reaches equilibrium, its final temperature will be the same.
- The mass of the water is 100 g, and the specific heat capacity of water is given as 4.19 kJ/(kg × K).
- To find the heat gained by the water, we use the formula:
Heat gained by water = mass × specific heat capacity × change in temperature
Heat gained by water = 100 g × 4.19 kJ/(kg × K) × (final temperature - 19°C)
2. Determine the heat lost by the steam:
- The initial temperature of the steam is unknown, but it will condense to water at 100°C (boiling point of water).
- The mass of the steam is given as 10 g, and the latent heat of vaporization for water is 2260 kJ/kg.
- To find the heat lost by the steam, we use the formula:
Heat lost by steam = mass × latent heat of vaporization
Heat lost by steam = 10 g × 2260 kJ/kg
3. Determine the heat gained by the aluminum cup:
- The specific heat capacity of aluminum is given as 922 J/(kg × K).
- The mass of the aluminum cup is given as 35 g.
- To find the heat gained by the aluminum cup, we use the formula:
Heat gained by aluminum cup = mass × specific heat capacity × change in temperature
Heat gained by aluminum cup = 35 g × 922 J/(kg × K) × (final temperature - 19°C)
4. Set up an equation for heat transfer:
- Since the aluminum cup and water are inside a perfectly insulating calorimetric container, the heat gained by the water and the aluminum cup must be equal to the heat lost by the steam.
- Equate the heat gained by the water and the aluminum cup to the heat lost by the steam:
Heat gained by water + Heat gained by aluminum cup = Heat lost by steam
5. Solve the equation for the final temperature:
- Substitute the values into the equation and solve for the final temperature.
Once you have the equation set up and the values substituted, you can solve it to find the final temperature of the water after equilibrium is reached.