What is the final temperature when 54g ice at 0oC is mixed with 200g water at 65oC
heat to melt ice + heat to raise T of melted ice to Tfinal + heat lost by warm water = 0
[mass ice x heat fusion] + [mass melted ice x specific heat H2o x (Tfinal-Tinitial)] + [mass warm water x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve. The only unknown is Tf.
To find the final temperature when ice and water are mixed, we can use the principle of conservation of energy, specifically the equation of heat transfer:
Q1 + Q2 = 0
where Q1 is the heat absorbed by the ice and Q2 is the heat released by the water.
The heat absorbed by the ice (Q1) can be calculated using the formula:
Q1 = m1 * c1 * ΔT1
where m1 is the mass of the ice, c1 is the specific heat capacity of ice, and ΔT1 is the change in temperature of the ice.
Given that the mass of the ice is 54g and the specific heat capacity of ice is 2.09 J/g°C, we can substitute these values into the formula:
Q1 = 54g * 2.09 J/g°C * (final temperature - 0°C)
The heat released by the water (Q2) can be calculated using a similar formula:
Q2 = m2 * c2 * ΔT2
where m2 is the mass of the water, c2 is the specific heat capacity of water, and ΔT2 is the change in temperature of the water.
Given that the mass of the water is 200g and the specific heat capacity of water is 4.18 J/g°C, we can substitute these values into the formula:
Q2 = 200g * 4.18 J/g°C * (final temperature - 65°C)
Now, since Q1 + Q2 = 0, we can set the equations equal to each other and solve for the final temperature:
54g * 2.09 J/g°C * (final temperature - 0°C) = -200g * 4.18 J/g°C * (final temperature - 65°C)
Simplifying the equation:
112.86 J°C * (final temperature - 0°C) = -836.00 J°C * (final temperature - 65°C)
Now, we can solve for the final temperature by isolating it on one side of the equation and simplifying:
112.86 J°C * final temperature = -836.00 J°C * final temperature - 54140 J°C
(112.86 J°C + 836.00 J°C) * final temperature = -54140 J°C
948.86 J°C * final temperature = -54140 J°C
final temperature = -54140 J°C / 948.86 J°C
final temperature ≈ -57.04°C
The final temperature when 54g of ice at 0°C is mixed with 200g of water at 65°C is approximately -57.04°C.