The water from two buckets is mixed together. One bucket contains 5kg of water at 20 degrees Celsius and the other contains 1kg of water at 80 degrees Celsius.
What is the final temperature of the mixture, assuming no heat is lost to the surroundings?
A. 30 degrees Celsius
B. 50 degrees Celsius
C. 60 degrees Celsius
D. 70 degrees Celsius
heat in = 5 (T-20)C
heat out = 1 (80 -T)C
so
5 T - 100 = 80 - T
6 T - 180
T = 30
@Damon what is the T in your answer??
Question
To find the final temperature of the mixture, we can use the principle of the conservation of energy. The law states that the total energy of an isolated system remains constant over time.
To solve this problem, we can use the concept of heat transfer. Heat transfer can be calculated using the equation:
Q = mcΔT
where Q is the heat transferred, m is the mass of the object, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, the heat transferred from the 80 degrees Celsius water to the final mixture can be expressed as:
Q1 = (1kg)(c)(ΔT1)
Similarly, the heat transferred from the 20 degrees Celsius water can be expressed as:
Q2 = (5kg)(c)(ΔT2)
Since the two buckets are mixed together, the final temperature will be the same for both.
We can set up an equation using the conservation of energy principle:
Q1 + Q2 = 0
Substituting the previous equations:
(1kg)(c)(ΔT1) + (5kg)(c)(ΔT2) = 0
Simplifying the equation:
(1kg)(c)(80 - Tf) + (5kg)(c)(20 - Tf) = 0
Multiplying and rearranging:
80 - Tf + 5(20 - Tf) = 0
Simplifying further:
80 - Tf + 100 - 5Tf = 0
Combining like terms:
180 - 6Tf = 0
Rearranging again:
6Tf = 180
Dividing by 6:
Tf = 30
Therefore, the final temperature of the mixture is 30 degrees Celsius.
The correct answer is option A: 30 degrees Celsius.