5.00 kg of some liquid at 10.0 oC is mixed with 1.00 kg of the same liquid at 40.0 oC. what is the final equilibrium temperature? ignore any heat flow with the containers and/or surroundings
the sum the heats gained is zero.
heat1+heat2=0
5*c*(Tf-10)+1*c*(tf-40)=0
c divides out, solve for Tf
tf(5+1)=50+40
tf= 90/6=15C
To find the final equilibrium temperature of the mixed liquids, we can use the principle of heat transfer known as the law of heat exchange, or the principle of calorimetry. Calorimetry is the science of measuring the heat associated with a chemical reaction or physical change.
The law of heat exchange states that the heat gained by a colder object equals the heat lost by a hotter object when they come into contact with each other until they reach thermal equilibrium.
In this particular case, we have two masses of the same liquid at different temperatures. Let's call the mass of the first liquid m1 and the mass of the second liquid m2. Also, let the initial temperature of the first liquid be T1 and the initial temperature of the second liquid be T2. We are required to find the final equilibrium temperature of the mixture, which we'll denote as Tf.
The total heat gained by the colder liquid equals the total heat lost by the hotter liquid. We can express this relationship mathematically using the formula:
m1 * c1 * (Tf - T1) = m2 * c2 * (T2 - Tf)
Where:
m1 and m2 are the masses of the first and second liquids, respectively.
c1 and c2 are the specific heat capacities of the liquid (assumed constant).
T1 and T2 are the initial temperatures of the first and second liquids, respectively.
Tf is the final equilibrium temperature of the mixture.
In this case, since both masses are the same liquid, the specific heat capacities (c1 and c2) are equal.
Now, we can substitute the given values into the equation. We have:
m1 = 5.00 kg
T1 = 10.0 °C
m2 = 1.00 kg
T2 = 40.0 °C
Substituting these values, we have:
5.00 * c * (Tf - 10.0) = 1.00 * c * (40.0 - Tf)
Since the specific heat capacities (c1 and c2) are the same, they cancel out.
Now, let's simplify the equation:
5.00 * (Tf - 10.0) = 40.0 - Tf
Expanding and rearranging the equation:
5.00 * Tf - 50.0 = 40.0 - Tf
Combining like terms:
6.00 * Tf = 90.0
Finally, solving for Tf:
Tf = 90.0 / 6.00
Tf = 15.0 °C
Therefore, the final equilibrium temperature of the mixture is 15.0 °C.