Suppose you mix 20.1 g of water at 66.2°C with 45.1 g of water at 35.7°C in an insulated cup. What is the maximum temperature of the solution after mixing?
heat lost by hot water + heat gained by cold water = 0
heat lostt or heat gain is
mass x specific heat x (Tfinal-Tinitial)
The molar heat capacity of silver is 25.35 . How much energy would it take to raise the temperature of 9.50 of silver by 10.5?
To find the maximum temperature of the solution after mixing, we can use the principle of conservation of energy. The heat lost by one substance is equal to the heat gained by another substance during the mixing process.
First, we need to calculate the heat lost (or gained) by each substance. We can use the equation:
q = mcΔT
Where:
- q is the heat absorbed or released by the substance (in joules, J)
- m is the mass of the substance (in grams, g)
- c is the specific heat capacity of the substance (in J/g°C)
- ΔT is the change in temperature (in °C)
Let's calculate the heat lost (or gained) by each substance in the mixture using their respective masses, specific heat capacities, and initial and final temperatures:
For the 20.1 g of water at 66.2°C:
q1 = m1cΔT1
Where:
- m1 = 20.1 g (mass of water 1)
- c = 4.18 J/g°C (specific heat capacity of water)
- ΔT1 = (Tf - Ti) = (Tf - 66.2°C), Tf being the final temperature
For the 45.1 g of water at 35.7°C:
q2 = m2cΔT2
Where:
- m2 = 45.1 g (mass of water 2)
- c = 4.18 J/g°C (specific heat capacity of water)
- ΔT2 = (Tf - Ti) = (Tf - 35.7°C), Tf being the final temperature
Since the heat lost by water 1 is equal to the heat gained by water 2, we can write:
q1 = q2
Therefore:
m1cΔT1 = m2cΔT2
Rearranging the equation, we have:
m1ΔT1 = m2ΔT2
Now let's substitute the values we have:
(20.1 g)(Tf - 66.2°C) = (45.1 g)(Tf - 35.7°C)
Simplifying the equation:
20.1Tf - (20.1)(66.2°C) = 45.1Tf - (45.1)(35.7°C)
Further simplification:
20.1Tf - 1328.62°C = 45.1Tf - 1605.07°C
Now, let's isolate Tf and solve for the final temperature:
20.1Tf - 45.1Tf = -1605.07°C + 1328.62°C
-25Tf = -276.45°C
Dividing by -25:
Tf ≈ 11.06°C
Therefore, the maximum temperature of the solution after mixing is approximately 11.06°C.