if 20g of steam at 100 c is mixed into 80 g of water at 20 c what is the final temperature if no heat lost
I answered this before but the question disappeared
Heat out of steam= 20 {2260+4.2(100-T)}
Heat into water = 80 (T-20)
so
4(T-20) = 2260 + 4.2(100-T)
4 T - 80 = 2260 + 4200 - 4.2 T
8.2 T = 6540
T = 797 which is silly of course
What it means is that 80 grams of water at 20 degrees simply can not condense 20 grams of steam. The final temp is 100 deg C and you still have some stem left :)
To determine the final temperature after mixing 20g of steam at 100°C with 80g of water at 20°C, we can use the principle of heat transfer.
First, we need to calculate the heat gained by the water and the heat lost by the steam. This can be determined using the equation:
Q = m * c * ΔT
Where:
Q = heat transfer (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
For the water:
Q (water) = m (water) * c (water) * ΔT (water)
For the steam:
Q (steam) = m (steam) * c (steam) * ΔT (steam)
Since no heat is lost to the surroundings, the heat gained by the water will be equal to the heat lost by the steam:
Q (water) = Q (steam)
Now, let's calculate the individual quantities:
m (water) = 80g
c (water) = 4.18 J/g°C (specific heat capacity of water)
ΔT (water) = final temperature (unknown) - initial temperature (20°C)
m (steam) = 20g
c (steam) = 2.03 J/g°C (specific heat capacity of steam)
ΔT (steam) = initial temperature (100°C) - final temperature (unknown)
Setting up the equation:
m (water) * c (water) * (final temperature - 20) = m (steam) * c (steam) * (100 - final temperature)
Plugging in the values:
80 * 4.18 * (final temperature - 20) = 20 * 2.03 * (100 - final temperature)
Now, we can solve for the final temperature.
To find the final temperature when steam is mixed with water without any heat loss, we can use the principle of conservation of energy.
The heat gained by the water and steam mix will be equal to the heat lost by the water and steam individually.
We can calculate the heat gained by the water using the formula:
Q = mcΔT
Where:
Q = heat gained (or lost) by the substance
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
In this case, we want to find the final temperature when the two substances are mixed. Since no heat is lost, the heat gained by the water and steam mix will be equal to zero.
Let's calculate the heat gained by the water and steam mix:
Heat gained by water = mcΔT = (80 g) * (4.18 J/g°C) * (Tf - 20°C)
Heat gained by steam = mcΔT = (20 g) * (2.03 J/g°C) * (Tf - 100°C)
Since the total heat gained is zero, we can set up the equation:
(80 g) * (4.18 J/g°C) * (Tf - 20°C) + (20 g) * (2.03 J/g°C) * (Tf - 100°C) = 0
By solving this equation, we can find the final temperature (Tf).