134 g of water at 7°C is added to ice at 0°C. If the final temperature of the system (which you can assume is isolated) is 0°C, determine HOW MUCH ICE MELTED. The specific heat of water is 4186 J/kg·°C. The latent heat of fusion for H2O is 335,000 J/kg.
To determine how much ice melted in this scenario, we need to calculate the amount of heat gained or lost by both the water and the ice.
First, let's calculate the heat lost by the water as it cools down from 7°C to 0°C. We'll use the formula:
Q = m * c * ΔT
Where:
Q is the heat gained or lost
m is the mass of the substance (water in this case)
c is the specific heat capacity of the substance (water in this case)
ΔT is the change in temperature
Given:
mass of water (m) = 134 g = 0.134 kg
specific heat capacity of water (c) = 4186 J/kg·°C
temperature change (ΔT) = (final temperature - initial temperature) = 0°C - 7°C = -7°C
Calculating the heat lost by the water:
Q_water = m * c * ΔT
Q_water = 0.134 kg * 4186 J/kg·°C * (-7°C)
Q_water = -3233.892 J
The negative sign indicates that heat is lost by the water.
Next, let's calculate the amount of ice melted. We'll use the formula:
Q = m * L
Where:
Q is the heat gained or lost
m is the mass of the substance (water that freezes or melts)
L is the specific latent heat of fusion for the substance (ice in this case)
Given:
specific latent heat of fusion for water (L) = 335,000 J/kg
Since the final temperature of the system is 0°C, we can assume that the ice melted completely, so the heat gained by the ice is equal to the heat lost by the water.
Calculating the heat gained by the ice:
Q_ice = Q_water = -3233.892 J
Using the formula:
Q_ice = m * L
We can rearrange to solve for the mass of ice (m):
m = Q_ice / L
m = -3233.892 J / 335,000 J/kg
m ≈ -0.00965 kg
Since mass cannot be negative, the magnitude of the mass is 0.00965 kg.
Therefore, approximately 0.00965 kg (or 9.65 grams) of ice melted in this system.
To determine how much ice melted, we can follow these steps:
Step 1: Calculate the heat gained by the water during the process when it warms up to 0°C.
Step 2: Calculate the heat lost by the ice during the process when it cools down from 0°C to its final temperature of 0°C.
Let's begin:
Step 1: Calculate the heat gained by the water:
The specific heat formula is Q = m * c * ΔT
where:
Q is the heat gained or lost
m is the mass
c is the specific heat
ΔT is the change in temperature
Q1 = m * c * ΔT
Q1 = 134 g * 4186 J/kg·°C * (0°C - 7°C)
Q1 = 134 g * 4186 J/kg·°C * (-7°C)
Q1 = -3193928 J
Note: The negative sign indicates that the water lost heat.
Step 2: Calculate the heat lost by the ice:
The heat lost by the ice is equal to the heat gained by the water and will be given by the following equation:
Q2 = m * L
where:
Q2 is the heat lost by the ice
m is the mass of ice melted
L is the latent heat of fusion
We need to find the mass of the ice melted, so let's rearrange the equation:
m = Q2 / L
Using the value of Q1 from Step 1 and the given value of L:
m = -3193928 J / 335000 J/kg
m ≈ -9.5 kg
Since mass cannot be negative, we can conclude that no ice melted during the process.