What is the final equilibrium temperature
when 5 g of milk at 13â—¦C is added to 161 g of coffee at 81â—¦C? Assume the specific heats of milk and coffee are the same as that of water, and neglect the specific heat of the container. Answer in units of â—¦C.
I got 83.18 C as the final temp but it says i got it incorrect. Did I answer the question incorrectly? (Damon this is the last one)
To find the final equilibrium temperature, you can use the principle of conservation of energy, assuming no heat is lost to the surroundings.
The amount of heat gained by the milk can be calculated using the equation:
Q_milk = (mass_milk) x (specific heat_milk) x (change in temperature)
Similarly, for the coffee:
Q_coffee = (mass_coffee) x (specific heat_coffee) x (change in temperature)
Since the final temperature will be the same for both substances in equilibrium, we can set the two equations equal to each other:
(mass_milk) x (specific heat_milk) x (change in temperature) = (mass_coffee) x (specific heat_coffee) x (change in temperature)
In this case, the specific heat capacity of milk and coffee are assumed to be the same as that of water, which is 4.184 J/(g°C).
Given:
mass_milk = 5 g
initial temperature_milk = 13°C
mass_coffee = 161 g
initial temperature_coffee = 81°C
Let's calculate the change in temperature first.
change in temperature = (initial temperature_coffee) - (initial temperature_milk)
= 81°C - 13°C
= 68°C
Now substitute the values into the equation:
(5 g) x (4.184 J/(g°C)) x (change in temperature) = (161 g) x (4.184 J/(g°C)) x (change in temperature)
Simplifying the equation:
(20.92 J/°C) x (68°C) = (677.524 J/°C) x (change in temperature)
1419.76 J = (677.524 J/°C) x (change in temperature)
Dividing both sides by (677.524 J/°C):
(change in temperature) = 1419.76 J / (677.524 J/°C)
(change in temperature) ≈ 2.094 °C
Now we can find the final temperature by adding the change in temperature to the initial temperature of milk:
final temperature = (initial temperature_milk) + (change in temperature)
≈ 13°C + 2.094°C
≈ 15.094°C
Therefore, the final equilibrium temperature is approximately 15.094°C.
If you obtained a different answer, please double-check your calculations.