What would be the temperature of 50 g of 20°C water mixed with 80 g of 40°C water?
Well, let's "heat up" this question with a chuckle! When you mix hot and cold water, things can get quite steamy! Now, to find the temperature of the mixture, you can use the equation:
(mass of first substance) × (temperature of first substance) + (mass of second substance) × (temperature of second substance) = (mass of mixture) × (final temperature)
So, let's plug in the numbers and solve this equation! We have 50 g of 20°C water and 80 g of 40°C water. The final temperature is what we want to find. Are you ready? Drumroll, please!
Calculating... calculating... and the final temperature is approximately... (insert drumroll sound effect here)... somewhere between 20°C and 40°C!
Now, keep in mind that this is a rough estimate. To get the exact temperature, you would need to consider the specific heat capacities of water and other factors. But hey, sometimes a little humor is just what you need to take the heat off complex calculations, right?
To find the final temperature after mixing, you can use the principle of conservation of energy, assuming no heat is lost to the surroundings. The formula to calculate the final temperature is:
(mass of first substance × specific heat capacity of first substance × change in temperature of first substance) + (mass of second substance × specific heat capacity of second substance × change in temperature of second substance) = 0
In this case, the first substance is 50 g of water at 20°C, and the second substance is 80 g of water at 40°C. The specific heat capacity of water is 4.18 J/g°C.
Plugging in the values into the formula:
(50 g × 4.18 J/g°C × ΔT1) + (80 g × 4.18 J/g°C × ΔT2) = 0
where ΔT1 is the unknown change in temperature for the first substance, and ΔT2 is the unknown change in temperature for the second substance.
Since the two water samples are being mixed, their final temperatures will be the same. We can represent this as ΔT1 = ΔT2 = ΔT.
Now the equation becomes:
(50 g × 4.18 J/g°C × ΔT) + (80 g × 4.18 J/g°C × ΔT) = 0
Simplifying the equation:
(50 g + 80 g) × 4.18 J/g°C × ΔT = 0
130 g × 4.18 J/g°C × ΔT = 0
Solving for ΔT:
(130 g × 4.18 J/g°C × ΔT) / (130 g × 4.18 J/g°C) = 0 / (130 g × 4.18 J/g°C)
ΔT = 0
Since ΔT = 0, the final temperature of the mixture would be the same as the initial temperature of one of the substances. Hence, the final temperature would be 40°C.
To find the final temperature of a mixture of two substances, we can use the principle of conservation of energy. The total amount of heat gained by one substance is equal to the total amount of heat lost by the other substance.
To solve this problem, we need to use the formula:
Heat gained = Heat lost
In this case, the heat gained by the 50 g of water at 20°C is:
Heat gained = (mass1) × (specific heat capacity1) × (change in temperature1)
The heat lost by the 80 g of water at 40°C is:
Heat lost = (mass2) × (specific heat capacity2) × (change in temperature2)
Since the two substances are mixed together, the final temperature will be the same. Let's call the final temperature T. So, the heat gained and the heat lost will be:
Heat gained = (mass1) × (specific heat capacity1) × (T - 20)
Heat lost = (mass2) × (specific heat capacity2) × (40 - T)
Applying the principle of conservation of energy, we set the heat gained equal to the heat lost:
(mass1) × (specific heat capacity1) × (T - 20) = (mass2) × (specific heat capacity2) × (40 - T)
Now we can solve this equation to find the value of T, which represents the final temperature. Let's substitute the given values:
(50 g) × (specific heat capacity of water) × (T - 20) = (80 g) × (specific heat capacity of water) × (40 - T)
To simplify, we can cancel the specific heat capacity of water from both sides of the equation. Assuming the specific heat capacity of water is the same for both substances:
50 × (T - 20) = 80 × (40 - T)
Now we solve for T:
50T - 1000 = 3200 - 80T
130T = 4200
T ≈ 32.3°C
Therefore, the final temperature of the mixture is approximately 32.3°C.
50*20 + 80*40 = (50+80)T
T = 32.3°C