A sample of steam with a mass of 0.550 g and at a temperature of 100 degrees C condenses into an insulated container holding 4.40 g of water at 5.0 degrees C. Assuming that no heat is lost to the surroundings, what will be the final temperature of the mixture?
calcualte the enthalpy change for the process in which 6.00g of steam at 100C is coverted to liquid water at a temperature of 35.0C
To find the final temperature of the mixture, you need to use the principle of heat transfer. The heat lost by the steam during the process of condensation will be equal to the heat gained by the water when it is heated. 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
ΔT is the change in temperature
First, let's calculate the heat lost by the steam when it condenses:
Q_lost = m_steam × c_steam × ΔT_steam
where:
m_steam = 0.550 g (mass of the steam)
c_steam = specific heat capacity of steam
ΔT_steam = final temperature - initial temperature of the steam = 100 - final temperature
Since steam is at its boiling point and changes phase from gas to liquid during condensation, we need to use the specific heat of vaporization (c_vaporization) instead of the specific heat capacity. The specific heat of vaporization for steam is approximately 2260 J/g.
Q_lost = m_steam × c_vaporization
Next, let's calculate the heat gained by the water when it is heated:
Q_gain = m_water × c_water × ΔT_water
where:
m_water = 4.40 g (mass of the water)
c_water = specific heat capacity of water
ΔT_water = final temperature - initial temperature of the water = final temperature - 5.0
We can set Q_lost equal to Q_gain because the heat lost by the steam is gained by the water:
Q_lost = Q_gain
m_steam × c_vaporization = m_water × c_water × ΔT_water
Now, we can solve for the final temperature of the mixture (ΔT_water):
ΔT_water = m_steam × c_vaporization / (m_water × c_water)
Finally, we can substitute the given values into the equation to find the final temperature of the mixture. The specific heat capacity of water (c_water) is approximately 4.18 J/g°C.
ΔT_water = 0.550 g × 2260 J/g / (4.40 g × 4.18 J/g°C)
By canceling out the units and evaluating the expression, we find ΔT_water.
Now, we can determine the final temperature by adding this change in temperature to the initial temperature:
final temperature = initial temperature + ΔT_water
Substituting the known values, we can calculate the final temperature of the mixture.