If 75 g of ice at 0.0 C were added to 1.5 L of water at 75 C, what would be the final temperature of the mixture?
75 g ice is melted to produce 75 g water at zero C and that is mixed with 1.5 L water at 75 C.
(75g x heat fusion ice) + [mass water from ice x specific heat water x (Tfinal-Tinitial)] = 0
Solve for Tfinal.
To calculate the final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the hot water will be equal to the heat gained by the ice as it melts.
First, let's calculate the heat lost by the hot water:
Q1 = m1 * c1 * ΔT1
Where:
Q1 is the heat lost by the hot water
m1 is the mass of the hot water
c1 is the specific heat capacity of water
ΔT1 is the change in temperature of the hot water
Given that:
m1 = 1500 g (since 1.5 L of water has a mass of 1500 g)
c1 = 4.18 J/g°C (specific heat capacity of water)
ΔT1 = (final temperature - initial temperature)
Initial temperature of the water = 75°C
Now, let's calculate the heat gained by the ice:
Q2 = m2 * ΔHf
Where:
Q2 is the heat gained by the ice
m2 is the mass of the ice
ΔHf is the heat of fusion of ice (amount of heat required to melt one gram of ice)
Given that:
m2 = 75 g (mass of the ice)
ΔHf = 334 J/g (heat of fusion of ice)
According to the principle of conservation of energy, Q1 = Q2
m1 * c1 * ΔT1 = m2 * ΔHf
Rearranging the equation to find the final temperature:
final temperature = (m2 * ΔHf) / (m1 * c1) + initial temperature
Substituting the given values into the equation:
final temperature = (75 g * 334 J/g) / (1500 g * 4.18 J/g°C) + 75°C
final temperature = 2.223°C + 75°C
final temperature = 77.22°C
Therefore, the final temperature of the mixture would be approximately 77.22°C.
To determine the final temperature of the mixture, we can use the principle of conservation of energy.
1. First, let's find the amount of heat gained or lost by the ice and water separately. We can use the formula:
Q = mcΔT
where Q is the heat gained or lost, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
2. The heat gained or lost by the ice can be calculated using the formula:
Q_ice = m_ice * c_ice * ΔT_ice
where m_ice is the mass of the ice, c_ice is the specific heat capacity of ice (2.09 J/g°C), and ΔT_ice is the change in temperature from the initial temperature of 0.0°C to the final temperature.
Substituting the given values:
m_ice = 75 g
c_ice = 2.09 J/g°C
ΔT_ice = Tf - 0.0°C (Tf is the final temperature)
Q_ice = 75 g * 2.09 J/g°C * (Tf - 0.0°C) = 156.75 Tf
3. The heat gained or lost by the water can be calculated using the formula:
Q_water = m_water * c_water * ΔT_water
where m_water is the mass of the water, c_water is the specific heat capacity of water (4.18 J/g°C), and ΔT_water is the change in temperature from the initial temperature of 75°C to the final temperature.
Substituting the given values:
m_water = 1.5 L * 1000 g/L = 1500 g
c_water = 4.18 J/g°C
ΔT_water = Tf - 75°C
Q_water = 1500 g * 4.18 J/g°C * (Tf - 75°C) = 6270 Tf - 470250 J
4. According to the principle of conservation of energy, the heat lost by the water is equal to the heat gained by the ice:
Q_water = Q_ice
6270 Tf - 470250 J = 156.75 Tf
Simplifying the equation, we get:
6113.25 Tf = 470250 J
5. Dividing both sides of the equation by 6113.25, we find:
Tf = 76.99°C
Therefore, the final temperature of the mixture would be approximately 76.99°C.