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

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To find the final temperature of the water after equilibrium is reached, we need to consider the heat gained or lost by each component of the system.

First, let's find the heat gained or lost by the water. We can use the formula:

Q = m × c × ΔT

Where:
Q is the heat gained or lost
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature

For the water, the mass is 100 g and the specific heat capacity is 4.19 kJ/(kg × K). The initial temperature of the water is 19°C, and the final temperature is unknown. So, ΔT for the water is the difference between the final temperature and the initial temperature.

Now, let's find the heat gained or lost by the aluminum cup. We can use the same formula:

Q = m × c × ΔT

For the aluminum cup, the mass is 35 g and the specific heat capacity is 922 J/(kg × K). The initial temperature of the cup is 19°C, and the final temperature is the same as the final temperature of the water.

Next, let's consider the heat released by the steam as it condenses into water. The heat released is given by:

Q = mass × latent heat of condensation

The mass of steam is 10 g, and the latent heat of condensation (latent heat of vaporization) for water is 2260 kJ/kg.

Finally, we can set up the equation to solve for the final temperature:

(Q of water + Q of aluminum cup) = Q of steam

Now we can substitute the formulas and given values to solve for the final temperature.