What would be the final temperature when 125g of 25 degrees Celcius water is mixed with 85g of 45 Degrees Celcius water? ( hint: Equate the heat gained by the cool water with the heat lost by the warm water.)
To find the final temperature when two substances are mixed, we can apply the principle of heat transfer, which states that the heat lost by one substance is equal to the heat gained by the other substance.
Let's assume the final temperature is 'T' degrees Celsius.
To solve this problem, we need to calculate the heat lost by the warm water and the heat gained by the cool water. We can then set these two values equal to each other and solve for 'T'.
The heat lost by the warm water can be calculated using the formula:
Q_lost = m1 * c1 * (T1 - T)
Where:
m1 = mass of the warm water (85g)
c1 = specific heat capacity of water (4.18 J/g°C, approximately)
T1 = initial temperature of the warm water (45°C)
The heat gained by the cool water can be calculated using the formula:
Q_gained = m2 * c2 * (T - T2)
Where:
m2 = mass of the cool water (125g)
c2 = specific heat capacity of water (4.18 J/g°C, approximately)
T2 = initial temperature of the cool water (25°C)
Since the principle of heat transfer states that the heat lost is equal to the heat gained, we can equate these two values:
Q_lost = Q_gained
m1 * c1 * (T1 - T) = m2 * c2 * (T - T2)
Now, we can substitute the given values:
(85g) * (4.18 J/g°C) * (45°C - T) = (125g) * (4.18 J/g°C) * (T - 25°C)
Simplifying the equation:
(85 * 4.18 * 45 - 85 * 4.18 * T) = (125 * 4.18 * T - 125 * 4.18 * 25)
Now, we can solve this equation to find the value of 'T' by isolating the 'T' term on one side:
(85 * 4.18 * 45) - (125 * 4.18 * 25) = 85 * 4.18 * T + 125 * 4.18 * T
Now, we can solve for 'T':
Simplifying the equation:
(85 * 4.18 * 45) - (125 * 4.18 * 25) = (85 + 125) * 4.18 * T
Now, divide both sides of the equation by [(85 + 125) * 4.18]:
([(85 * 4.18 * 45) - (125 * 4.18 * 25)] / [(85 + 125) * 4.18]) = T
After evaluating this expression, you will find the final temperature 'T'.