Suppose 0.0210 kg of steam (at 100.00°C) is added to 0.210 kg of water (initially at 19.5°C.). The water is inside a copper cup of mass 48.9 g. The cup is inside a perfectly insulated calorimetry container that prevents heat flow with the outside environment. Find the final temperature (in °C) of the water after equilibrium is reached.

Question

Suppose 0.0210 kg of steam (at 100.00°C) is added to 0.210 kg of water (initially at 19.5°C.). The water is inside a copper cup of mass 48.9 g. The cup is inside a perfectly insulated calorimetry container that prevents heat flow with the outside environment. Find the final temperature (in °C) of the water after equilibrium is reached.

use the following values:
c_copper=0.386 kJ/kg.K
c_water=4.19 kJ/kg.K
L_fusion=2.26 MJ/kg

Answer 1

To find the final temperature of the water after equilibrium is reached, we can use the principle of conservation of energy. The heat gained by the water and the cup will be equal to the heat lost by the steam.

Let's break down the problem step by step:

Step 1: Calculate the heat gained by the water.
The heat gained by the water can be calculated using the formula:
Q_water = m_water * c_water * ΔT_water
where:
m_water = mass of the water
c_water = specific heat capacity of water
ΔT_water = change in temperature of the water

Given:
m_water = 0.210 kg
c_water = 4.19 kJ/kg.K
ΔT_water = final temperature of water - initial temperature of water

Step 2: Calculate the heat gained by the cup.
The heat gained by the cup can be calculated using the formula:
Q_cup = m_cup * c_copper * ΔT_cup
where:
m_cup = mass of the cup
c_copper = specific heat capacity of copper
ΔT_cup = change in temperature of the cup

Given:
m_cup = 48.9 g = 0.0489 kg
c_copper = 0.386 kJ/kg.K
ΔT_cup = final temperature of the cup - initial temperature of the cup = ΔT_water (since the cup and water will reach the same temperature at equilibrium)

Step 3: Calculate the heat lost by the steam.
The heat lost by the steam can be calculated using the formula:
Q_steam = m_steam * L_vaporization
where:
m_steam = mass of the steam
L_vaporization = latent heat of vaporization

Given:
m_steam = 0.021 kg
L_vaporization = 2.26 MJ/kg = 2.26 * 10^6 J/kg

Step 4: Equate the heat gained by the water and cup to the heat lost by the steam.
Q_water + Q_cup = Q_steam

Step 5: Solve for the final temperature of the water.
Rearranging the equation, we have:
(m_water * c_water * ΔT_water) + (m_cup * c_copper * ΔT_water) = (m_steam * L_vaporization)

Now plug in the given values and solve the equation for ΔT_water, which represents the change in temperature of water.

Finally, the final temperature of the water can be calculated by adding ΔT_water to the initial temperature of the water.

Note: Make sure to convert all units to a consistent system, such as SI units, before performing the calculations.