600g of water is mixed with 20g of steam at 100 deg Celcius. What is the final temperature if the original temperature of the water is 25 deg Celcius
The 20 g of steam will transfer 20g*540 Cal/g of heat to the liquid water while condensing. That makes 10,800 Cal, which is enough to raise the liquid water temperature by 18 C, to 38 C. As a final step, calculate the equilbrium temp T when mixing 600g liquid H2O at 38 C with 20 g of liquid H2O at at 100 C.
600(T - 38) = 20(100 - T)
Solve for T
To find the final temperature when water and steam are mixed, you can use the principle of energy conservation. The total energy before and after the mixing should remain the same.
First, calculate the energy of the water before the mixing using the specific heat capacity formula:
Energy = mass × specific heat capacity × change in temperature
Given:
Mass of water = 600g
Specific heat capacity of water = 4.18 J/g°C
Initial temperature of water = 25°C
Final temperature (unknown) = ?
Energy of the water before mixing = 600g × 4.18 J/g°C × (final temperature - 25°C)
Next, calculate the energy of the steam before the mixing. Since the steam is at 100°C, it is already in its gaseous state and does not need to undergo any temperature change. Therefore, the energy of the steam before mixing is:
Energy of the steam before mixing = mass × specific heat capacity × temperature
Given:
Mass of steam = 20g
Specific heat capacity of steam = 2.03 J/g°C
Temperature of steam = 100°C
Energy of the steam before mixing = 20g × 2.03 J/g°C × 100°C
Since energy is conserved, the total energy before and after the mixing should be equal. Therefore, we can set up an equation:
Energy of the water before mixing + Energy of the steam before mixing = Total energy after mixing
600g × 4.18 J/g°C × (final temperature - 25°C) + 20g × 2.03 J/g°C × 100°C = Total energy after mixing
Now you can solve this equation to find the final temperature after the mixing. Rearrange the equation and isolate the final temperature term:
600g × 4.18 J/g°C × (final temperature - 25°C) = Total energy after mixing - 20g × 2.03 J/g°C × 100°C
Dividing both sides of the equation by (600g × 4.18 J/g°C) will result in:
final temperature - 25°C = (Total energy after mixing - 20g × 2.03 J/g°C × 100°C) / (600g × 4.18 J/g°C)
Finally, add 25°C to both sides of the equation to solve for the final temperature:
final temperature = [(Total energy after mixing - 20g × 2.03 J/g°C × 100°C) / (600g × 4.18 J/g°C)] + 25°C
Please note that the specific heat capacities used in the calculations are approximate values commonly used for water and steam and may vary slightly depending on the conditions.