Determine the final temperature when 10g of steam at 100C mixes with 500g of water at 25C.
I have 4.184x 10(100-x) + 40700 x 10= 500 x (x-25) x 4.18.
The book has 10/18 instead of 10 on left hand side of equation. Why??
I expect the 18 is to convert 10 g H2O to mols since the 40700 is in J/mol and not J/g.
The left hand side of the equation represents the heat gained or lost by the substances involved in the mixing process. In this case, it is necessary to convert the mass of steam from grams to moles in order to properly calculate this value.
The molar mass of water is approximately 18 g/mol. Therefore, 10 grams of steam represents (10/18) moles of water. Similarly, the molar mass of water is approximately 18 g/mol, so 500 grams of water is equal to (500/18) moles of water.
Hence, the correct equation should be:
4.184 * 10 * (100-x) + 40700 * (10/18) = 500 * (x-25) * 4.18
The factor of (10/18) in front of the left-hand side of the equation accounts for the conversion of grams to moles for the mass of steam.
The reason the book has 10/18 instead of 10 on the left-hand side of the equation is because it's accounting for the fact that the steam is initially in the form of water vapor at 100°C. Water vapor has a different specific heat capacity compared to liquid water.
In the equation you provided, the left-hand side represents the heat absorbed by the steam and the right-hand side represents the heat released by the water. Here's a step-by-step explanation of the equation:
1. The left-hand side:
- The term "4.184" represents the specific heat capacity of water in joules per gram-kelvin (J/g°C).
- "10" represents the mass of the steam in grams.
- "(100-x)" represents the temperature change of the steam, which starts at 100°C and ends at "x"°C. The change in temperature is given by 100 - x.
- Multiplying these three values together gives you the total heat absorbed by the steam.
2. The right-hand side:
- The term "500" represents the mass of the water in grams.
- "(x-25)" represents the temperature change of the water, which starts at 25°C and ends at "x"°C. The change in temperature is given by x - 25.
- "4.18" represents the specific heat capacity of water in joules per gram-kelvin (J/g°C).
- Multiplying these three values together gives you the total heat released by the water.
By setting the two sides of the equation equal to each other, you are equating the heat absorbed by the steam to the heat released by the water. Solving this equation will give you the value of "x," which represents the final temperature when the steam and water mix.
Regarding the different values in the book's equation, it's possible that the book is using a different specific heat capacity value for water vapor. It's important to note that the specific heat capacity of water vapor is higher than that of liquid water, so using different values may lead to slightly different results.