If 9.30 x 10^5 J of energy are transferred to 2.00kg of ice at 0 deg C, what is the final temperature of the system?
To find the final temperature of the system, we need to determine the amount of energy required to raise the temperature of the ice from 0°C to the final temperature.
First, let's calculate the energy required to raise the temperature of the ice to its melting point (0°C). The specific heat capacity of ice is 2.09 J/(g°C).
Since the mass of the ice is 2.00 kg, we need to convert it to grams by multiplying it by 1000:
2.00 kg * 1000 g/kg = 2000 g.
Now we can calculate the energy required to raise the temperature of the ice to 0°C:
Energy = mass * specific heat capacity * change in temperature
= 2000 g * 2.09 J/(g°C) * (0°C - 0°C)
= 0 J.
Therefore, no energy is required to raise the temperature of the ice from its initial temperature to 0°C.
Next, the energy transferred to the system (9.30 x 10^5 J) is used to melt the ice at 0°C. The heat of fusion for ice is 334 J/g.
To find the amount of ice that will be melted, we divide the energy transferred by the heat of fusion:
Amount of ice melted = energy transferred / heat of fusion
= 9.30 x 10^5 J / 334 J/g
≈ 2784 g.
Since the initial mass of the ice is 2000 g, and the amount of ice that will be melted is 2784 g, we need to subtract the mass of the melted ice from the initial mass:
Final mass of the ice = initial mass - mass of melted ice
= 2000 g - 2784 g
= -784 g.
However, a negative final mass doesn't make sense physically, indicating that all the ice has melted.
Since all the ice has melted, the final temperature will be 0°C, because the water will be in its solid-liquid equilibrium state.
To find the final temperature of the system, first, we need to determine the amount of energy required to melt the ice and then find the remaining energy to calculate the temperature.
Step 1: Calculate the energy required to melt the ice:
The energy required to melt 1 kg of ice is known as the latent heat of fusion and is approximately 3.34 x 10^5 J/kg.
Energy required to melt 2.00 kg of ice = (3.34 x 10^5 J/kg) x (2.00 kg) = 6.68 x 10^5 J
Step 2: Calculate the remaining energy after melting the ice:
Remaining energy = Total energy - Energy used to melt the ice
Remaining energy = (9.30 x 10^5 J) - (6.68 x 10^5 J) = 2.62 x 10^5 J
Step 3: Calculate the change in temperature using the specific heat capacity:
The specific heat capacity of ice is approximately 2.09 J/g°C.
Change in temperature = Remaining energy / (mass x specific heat capacity)
= (2.62 x 10^5 J) / (2.00 kg x 2.09 J/g°C x 1000 g/kg)
= 62.96 °C
Step 4: Calculate the final temperature:
Final temperature = Initial temperature + Change in temperature
Final temperature = 0 °C + 62.96 °C = 62.96 °C
Therefore, the final temperature of the system is approximately 62.96 °C.