When you take a bath, how many kilograms of hot water (48°C) must you mix with cold water (13°C) so that the temperature of the bath is 36°C? The total mass of water (hot plus cold) is 185 kg. Ignore any heat flow between the water and its external surroundings.
When you are taking a bath, how many kilograms of hot water at 48oC must you mix with cold water at 12oC so that the temperature of the bath is 36oC? Assume the total mass of water (hot water + cold water) is 90kg.
If the water of the bath must be 67°C,by how much must the water be cooled or heated or heated?
Call mass hot water H.
Then mass cold water is 185-H.
H*specific heat water x (Tfinal-Tinitial) + (185-H)*specific heat water x (Tfinal-Tinitial) = 0
Solve for H and C.
Check my thinking. Post your work if you get stuck.
To solve this problem, we need to apply the principle of heat transfer, which states that the heat gained by the cold water is equal to the heat lost by the hot water.
Let's determine the amount of heat gained by the cold water and the amount of heat lost by the hot water. We can use the equation:
Q = mcΔT,
where Q is the heat gained or lost, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.
For the cold water:
Qcold = mcoldΔTcold.
Similarly, for the hot water:
Qhot = mhotΔThot.
Since both Qcold and Qhot are equal, we can set them equal to each other:
mcoldΔTcold = mhotΔThot.
We know that the final temperature of the bath is 36°C, so:
ΔThot = 36°C - 48°C = -12°C,
ΔTcold = 36°C - 13°C = 23°C.
We also know that the total mass of water is 185 kg, so:
mhot + mcold = 185 kg.
Now, we can substitute the values into the equation and solve for mcold.
mcold(23°C) = mhot(-12°C).
Since mcold = 185 kg - mhot, we can substitute that in:
(185 kg - mhot)(23°C) = mhot(-12°C).
Simplify the equation:
4255 kg°C - 23 mcold = -12 mhot.
Rearrange the equation:
35 mcold + 12 mhot = 4255 kg°C.
Since mcold = 185 kg - mhot, substitute it in:
35(185 kg - mhot) + 12 mhot = 4255 kg°C.
Expand and solve for mhot:
6485 kg - 35 mhot + 12 mhot = 4255 kg°C.
Combine the like terms:
-23 mhot = -2230 kg°C.
Divide by -23:
mhot = 97 kg.
Therefore, you would need 97 kg of hot water (48°C) to mix with the cold water (13°C) to achieve a bath temperature of 36°C.