Final temp of a block of iron if 0.87g of water condenses on a 85.0g block of iron that is initially at 20 degrees Celsius.
To calculate the final temperature of the block of iron, we need to determine the amount of heat transferred from the condensing water to the block of iron.
To do this, we can use the heat transfer equation:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
First, let's calculate the heat transferred from the water to the iron block.
Given:
Mass of water (m_w) = 0.87 g
Mass of iron block (m_i) = 85.0 g
Initial temperature (T_i) of the iron block = 20 °C
The specific heat capacity of water at constant pressure is approximately 4.18 J/g°C. However, the specific heat capacity of iron is much lower, so we neglect its contribution in this case.
So, for the water, the equation becomes:
Q = m_wc_wΔT_w
where:
c_w is the specific heat capacity of water (4.18 J/g°C)
ΔT_w is the temperature change of the water. Since the water condenses, it changes from its boiling point (100 °C) to the final temperature.
Since we know that the water condenses, it initially starts at its boiling point (100 °C) and then changes to its final temperature.
The heat transferred from the water to the iron is equal to the heat transferred from the iron to the water. So, the equations can be set equal to each other:
m_wc_wΔT_w = m_ic_iΔT_i
Rearranging the equation, we can solve for ΔT_i (the change in temperature of the iron block):
ΔT_i = (m_wc_wΔT_w) / (m_i*c_i)
Now, let's put the values into the equation:
m_i = 85.0 g (mass of iron block)
c_i = specific heat capacity of iron (we will assume it to be 0.449 J/g°C, which is a reasonable approximation)
ΔT_w = T_i - 100 °C (Temperature difference of water)
After we have calculated ΔT_i, we can find the final temperature by subtracting this change in temperature from the initial temperature:
T_f = T_i - ΔT_i
Now, let's calculate the final temperature of the iron block.