If 10-kg of ice at 0 degrees Celsius is added to 2-kg of steam at 100 degrees Celsius, the temperature of the resulting mixture is? Use Joules. ANSWER: 40
Specific Heats:
Ice = 2060
Steam = 2020
Latent Heats:
Water melting = 3.33x10^5
Water boiling = 2.26x10^6
To find the final temperature of the resulting mixture, you can use the principle of conservation of energy. The total energy gained or lost in the system is equal to zero.
First, let's calculate the energy gained or lost by the ice as it warms up and melts:
1. Energy gained by ice to reach 0 degrees Celsius:
The specific heat capacity of ice is given as 2060 J/kg·°C.
The mass of the ice is 10 kg.
The initial temperature of the ice is -10 degrees Celsius (it's already below 0 degrees Celsius).
So, the energy gained by the ice to reach 0 degrees Celsius is:
Energy = (mass of ice) x (specific heat capacity of ice) x (change in temperature)
= 10 kg x 2060 J/kg·°C x (0°C - (-10°C))
= 10 kg x 2060 J/kg·°C x 10°C
= 206,000 J
2. Energy gained by ice as it melts at 0 degrees Celsius:
The latent heat of fusion (melting) of water is given as 3.33x10^5 J/kg.
So, the energy gained by the ice as it melts is:
Energy = (mass of ice) x (latent heat of fusion)
= 10 kg x 3.33x10^5 J/kg
= 3.33x10^6 J
Next, let's calculate the energy gained or lost by the steam as it cools down and condenses:
3. Energy lost by steam to reach 100 degrees Celsius:
The specific heat capacity of steam is given as 2020 J/kg·°C.
The mass of the steam is 2 kg.
The initial temperature of the steam is 100 degrees Celsius.
So, the energy lost by the steam to reach 100 degrees Celsius is:
Energy = (mass of steam) x (specific heat capacity of steam) x (change in temperature)
= 2 kg x 2020 J/kg·°C x (100°C - 100°C)
= 0 J
4. Energy lost by steam as it condenses:
The latent heat of vaporization (boiling) of water is given as 2.26x10^6 J/kg.
So, the energy lost by the steam as it condenses is:
Energy = (mass of steam) x (latent heat of vaporization)
= 2 kg x 2.26x10^6 J/kg
= 4.52x10^6 J
Now, let's calculate the final temperature of the resulting mixture:
Total energy gained = Energy gained by the ice - Energy lost by the steam
Total energy gained = (206,000 J + 3.33x10^6 J) - (0 J + 4.52x10^6 J)
Total energy gained = 206,000 J + 3.33x10^6 J - 4.52x10^6 J
Total energy gained = -890,000 J
Since the total energy gained is negative, it means that the system lost energy. To find the resulting temperature, we can divide the total energy gained by the sum of the masses of the ice and steam:
Resulting temperature = (Total energy gained) / (mass of ice + mass of steam)
Resulting temperature = (-890,000 J) / (10 kg + 2 kg)
Resulting temperature = (-890,000 J) / 12 kg
Resulting temperature = -74,166.67 J/kg
Hence, the resulting temperature of the mixture is approximately -74,166.67 degrees Celsius.