If 10kg of ice at 0 degrees celsius is added to 2kg of steam
at 100 degrees celsius.Calculate the resulting temperature of the mixture
idk also
To calculate the resulting temperature of the mixture, we can use the principle of conservation of energy.
1. First, let's calculate the heat gained by the ice:
The heat gained by the ice is given by the formula Q = m * c * ΔT, where Q is the heat gained, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
For ice, the specific heat capacity (c) is 2.09 J/g°C, and the change in temperature (ΔT) is the final temperature of the mixture minus the initial temperature of the ice (final temperature - 0°C).
Given that the mass of the ice (m) is 10 kg (which is equal to 10,000 grams), and the initial temperature of the ice is 0°C, we can calculate the heat gained by the ice as follows:
Q_ice = m * c * ΔT_ice
= 10,000 g * 2.09 J/g°C * (T_final - 0°C)
2. Next, let's calculate the heat lost by the steam:
The heat lost by the steam can be calculated using the same formula as above, but this time with the mass and initial temperature of the steam.
For steam, the specific heat capacity (c) is 1.996 J/g°C, and the change in temperature (ΔT) is the final temperature of the mixture minus the initial temperature of the steam (final temperature - 100°C).
Given that the mass of the steam (m) is 2 kg (which is equal to 2,000 grams), and the initial temperature of the steam is 100°C, we can calculate the heat lost by the steam as follows:
Q_steam = m * c * ΔT_steam
= 2,000 g * 1.996 J/g°C * (T_final - 100°C)
3. Finally, we can set the heat gained by the ice equal to the heat lost by the steam and solve for the final temperature (T_final).
Q_ice = Q_steam
10,000 g * 2.09 J/g°C * (T_final - 0°C) = 2,000 g * 1.996 J/g°C * (T_final - 100°C)
Simplifying this equation, we can solve for T_final:
20,9000 (T_final - 0°C) = 3,992(T_final - 100°C)
20,9000 T_final - 0°C = 3,992 T_final - 399,200°C
3,992 T_final - 20,900 T_final = -399,200°C
-16,908 T_final = -399,200°C
T_final = -399,200°C / -16,908
T_final ≈ 23.7°C
Therefore, the resulting temperature of the mixture is approximately 23.7 degrees Celsius.
To calculate the resulting temperature of the mixture, we can use the principle of energy conservation. The heat gained by the ice will be equal to the heat lost by the steam.
First, we need to calculate the heat gained by the ice. To do this, we use the formula:
Qice = m × c × ΔT
Where:
Qice = heat gained by the ice (in Joules)
m = mass of the ice (in kg)
c = specific heat capacity of ice (approximately 2,093 J/kg°C)
ΔT = change in temperature of the ice (final temperature - initial temperature)
The mass of the ice is given as 10 kg, and the initial temperature of the ice is 0°C. The final temperature of the mixture will be the same for both the ice and steam, so we can represent it as T.
Qice = 10 kg × 2,093 J/kg°C × (T°C - 0°C)
= 20,930 J°C × T
Next, we calculate the heat lost by the steam. To do this, we use the formula:
Qsteam = m × c × ΔT
Where:
Qsteam = heat lost by the steam (in Joules)
m = mass of the steam (in kg)
c = specific heat capacity of steam (approximately 2,000 J/kg°C)
ΔT = change in temperature of the steam (final temperature - initial temperature)
The mass of the steam is given as 2 kg, and the initial temperature of the steam is 100°C. The final temperature of the mixture will be the same for both the ice and steam, so we can represent it as T.
Qsteam = 2 kg × 2,000 J/kg°C × (T°C - 100°C)
= 4,000 J°C × (T - 100)
Since the heat gained by the ice is equal to the heat lost by the steam, we can set up an equation:
20,930 J°C × T = 4,000 J°C × (T - 100)
Now, we can solve this equation to find the value of T, which represents the final temperature of the mixture.
20,930 T = 4,000 T - 400,000
16,930 T = -400,000
T = -400,000 / 16,930
T ≈ -23.64
The resulting temperature of the mixture is approximately -23.64 degrees Celsius.