100g of water at 30.0C is mixed with 150g of water at 85.0C. What is the final temperature of th mixture assuming no heat is gained or lost during the mixing process?
The sum of heats gained is zero (some of heats gained is negative,or lost).
Heat100g gained+Heat150gained=0
100*c*(Tf-30C)+150*c*(Tf-85)=0
solve for Tf
ice, 5,
To find the final temperature of the mixture, we can use the principle of conservation of energy, which states that the total amount of energy in an isolated system remains constant.
To solve this problem, we can use the principle of energy conservation, which states that the energy gained by the colder water (Qc) is equal to the energy lost by the hotter water (Qh).
The equation to find the energy gained or lost by an object is given by:
Q = mcΔT,
where Q is the energy gained or lost, m is the mass of the object, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
First, let's calculate the energy lost by the hotter water (Qh):
Qh = (mass of hot water) x (specific heat capacity of water) x (change in temperature)
= 150g x 4.186 J/g°C x (85.0°C - Tf), where Tf is the final temperature of the mixture.
Next, let's calculate the energy gained by the colder water (Qc):
Qc = (mass of cold water) x (specific heat capacity of water) x (change in temperature)
= 100g x 4.186 J/g°C x (Tf - 30.0°C)
According to the principle of energy conservation, Qc = Qh:
100g x 4.186 J/g°C x (Tf - 30.0°C) = 150g x 4.186 J/g°C x (85.0°C - Tf)
Now, let's solve the equation for Tf:
100g x 4.186 J/g°C x Tf - 100g x 4.186 J/g°C x 30.0°C = 150g x 4.186 J/g°C x 85.0°C - 150g x 4.186 J/g°C x Tf
400.74 Tf - 12505.2 = 62395.5 - 626.16 Tf
Combining the like terms and rearranging the equation:
400.74 Tf + 626.16 Tf = 62395.5 + 12505.2
1026.9 Tf = 74868.7
Tf = 74868.7 / 1026.9
Tf ≈ 73.0°C
Therefore, the final temperature of the mixture is approximately 73.0°C.