If 40.0 g of water at 70 degrees C is mixed with 40.0 g of ethanol at 10.0 degrees C, what is the final temperature of the mixture?
How does one go about solving this problem? I found the specific heat of water and ethanol, but now what?
To solve this problem, you need to use the principle of energy conservation. The total heat gained by the water and ethanol mixture will be equal to the total heat lost by the water and ethanol individually.
First, you can calculate the heat gained or lost by each substance using the formula Q = mcΔT, where Q is the heat gained or lost, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.
For the water:
Q_water = m_water * c_water * ΔT_water
For the ethanol:
Q_ethanol = m_ethanol * c_ethanol * ΔT_ethanol
Since the water and ethanol are mixed, their final temperatures will be the same, so you can set Q_water equal to -Q_ethanol (since heat lost is negative heat gained) and solve for the final temperature.
Q_water = -Q_ethanol
m_water * c_water * ΔT_water = -m_ethanol * c_ethanol * ΔT_ethanol
Substituting the given values:
40.0 g * c_water * (final temperature of water - 70°C) = -40.0 g * c_ethanol * (final temperature of ethanol - 10.0°C)
Now, if you have the specific heat values for water and ethanol, you can plug them in and solve the equation for the final temperature.
Once you know the final temperature of either water or ethanol, you can use the principle of energy conservation to determine the final temperature of the mixture by assuming that the heat lost by one substance is completely gained by the other.
So, the final temperature of the mixture will be the same as the final temperature of either water or ethanol, depending on which substance you choose to calculate first.
Remember to pay attention to the signs (positive or negative) when plugging in the values and to use the correct units for mass and specific heat.