A 35.0 g block of copper at 350.0 degrees celcius is added to a beaker containing 525 g of water at 35.0 degrees celcius. What is the final temperature of water?
heat lost by Cu + heat gained by H2O = 0
[mass Cu x specific heat Cu x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial) = 0
Substitute and solve for Tf.
To find the final temperature of the water, we can use the principle of conservation of energy.
The heat gained by the water is equal to the heat lost by the copper block.
The heat gained or lost by an object can be calculated using the formula:
Q = m * c * ΔT
Where:
Q is the heat gained or lost
m is the mass of the object
c is the specific heat capacity of the material
ΔT is the change in temperature
For the water:
Q_water = m_water * c_water * ΔT_water
For the copper block:
Q_copper = m_copper * c_copper * ΔT_copper
Since the final temperature will be the same for both objects (once thermal equilibrium is reached), we can set the two equations equal to each other and solve for the final temperature of the water.
Q_water = Q_copper
Now let's plug in the given values:
m_water = 525 g (mass of water)
c_water = 4.18 J/g°C (specific heat capacity of water)
ΔT_water = final temperature of water - initial temperature of water
m_copper = 35.0 g (mass of copper block)
c_copper = 0.385 J/g°C (specific heat capacity of copper)
ΔT_copper = final temperature of water - initial temperature of copper block (350.0°C)
Since the initial temperature of the water is 35.0°C and the initial temperature of the copper block is 350.0°C, we can rewrite the equation:
Q_water = m_water * c_water * (final temperature of water - 35.0)
Q_copper = m_copper * c_copper * (35.0 - final temperature of water)
Setting Q_water equal to Q_copper:
m_water * c_water * (final temperature of water - 35.0) = m_copper * c_copper * (35.0 - final temperature of water)
Now, let's rearrange the equation to solve for the final temperature of the water:
m_water * c_water * final temperature of water - m_water * c_water * 35.0 = m_copper * c_copper * 35.0 - m_copper * c_copper * final temperature of water
m_water * c_water * final temperature of water + m_copper * c_copper * final temperature of water = m_water * c_water * 35.0 + m_copper * c_copper * 35.0
Combining like terms and grouping variables:
(final temperature of water) * (m_water * c_water + m_copper * c_copper) = 35.0 * (m_water * c_water + m_copper * c_copper)
Dividing both sides by the sum of the specific heat capacities:
(final temperature of water) = (35.0 * (m_water * c_water + m_copper * c_copper)) / (m_water * c_water + m_copper * c_copper)
Now, let's substitute the given values into the equation and calculate the final temperature of the water.