Steam of mass 11.0 g at 100°C is added to 126.7 g of ice at 0.00°C. Find the final temperature of the system.
Find these values in textbooks or google:
Hv = latent heat of vaporization
Hf = latent heat of fusion
c,water = specific heat of liquid water
Formula for energy: Q = m*c*(T2 - T1)
Summation of all energy is zero:
m,steam*Hv + m,steam(c,water)(T2-100) + m,ice(c,water)(T2-0) + m,ice*Hf = 0
m,steam = 11.0 g
m,ice = 126.7 g
T1 (ice) = 0 °C
T1 (steam) = 100 °C
Look first for the latent heats and specific heat values. Then everything is given so you can solve for T2. Units in °C.
To find the final temperature of the system, we can use the principle of conservation of energy:
1. First, let's consider the heat gained or lost by each component of the system.
- The heat gained by the steam is given by the equation: Q1 = mass * specific heat capacity * change in temperature.
- The mass of the steam is 11.0 g.
- The specific heat capacity of steam is constant and is approximately 2.03 J/g°C.
- The change in temperature is the final temperature - initial temperature, so it will be Tf - 100°C.
- The heat lost by the ice is given by the equation: Q2 = mass * specific heat capacity * change in temperature.
- The mass of the ice is 126.7 g.
- The specific heat capacity of ice is constant and is approximately 2.09 J/g°C.
- The change in temperature is the final temperature - 0.00°C, so it will be Tf - 0.00°C.
2. According to the principle of conservation of energy, the heat lost by the steam must be equal to the heat gained by the ice.
Therefore, Q1 = Q2.
3. Now we can substitute the values and set up the equation:
mass1 * specific heat capacity1 * (Tf - 100°C) = mass2 * specific heat capacity2 * (Tf - 0.00°C)
11.0 g * 2.03 J/g°C * (Tf - 100°C) = 126.7 g * 2.09 J/g°C * (Tf - 0.00°C)
4. Now we can solve the equation for Tf, which is the final temperature of the system.
11.0 g * 2.03 J/g°C * Tf - 11.0 g * 2.03 J/g°C * 100°C = 126.7 g * 2.09 J/g°C * Tf - 126.7 g * 2.09 J/g°C * 0.00°C
(11.0 g * 2.03 J/g°C - 126.7 g * 2.09 J/g°C) * Tf = 126.7 g * 2.09 J/g°C * 0.00°C - 11.0 g * 2.03 J/g°C * 100°C
(22.336 g * J/°C) * Tf = -2230.9 g * J/°C
5. Simplifying the equation, we have:
Tf = -2230.9 g * J/°C / (22.336 g * J/°C)
Tf ≈ -99.97°C
6. The final temperature of the system is approximately -99.97°C.
Note: Negative temperatures indicate a change from a hotter state to a colder state.