Suppose that 100.0 g of ice a 0 degreesC are added to 300.0 g of water at 25.0 degrees . Is this sufficient ice to lower the temperature of water to 5.00 degrees C and still have ice remaining? Calculate the energy (heat) which must be removed from water to achieve the desired temperature change, and the "prove" that there is or is not sufficient ice to cool the water. Use the specific heat capacity of water(4.184J/g*C) and the heat of fusion of ice (335 J/g).
so far i have 0.00055787= 4.184/(300)(25.00)
and 335/100= 3.35
but i don't know what these mean or how to even answer this question.
I would just do this. Find the final temperature. The sum of the heats gained is zero.
Heatmeltice+heatwarmicewater+heatwater=0
100Hf+100cw(Tf-0)+ 300cw(Tf-25)=0
solve this equation for Tf.
would now be the time to as you what Hf and cw mean?
To determine if there is sufficient ice to lower the temperature of water to 5.00°C and still have ice remaining, we need to calculate the amount of heat needed to cool the water to the desired temperature.
First, let's calculate the heat required to cool the water from 25.0°C to 5.00°C.
Heat = mass × specific heat capacity × temperature change
Heat = 300.0 g × 4.184 J/g·°C × (25.0°C - 5.00°C)
Heat = 300.0 g × 4.184 J/g·°C × 20.0°C
Heat = 2510.4 J
Therefore, we need to remove 2510.4 J of heat from the water to cool it to 5.00°C.
Now, let's determine the amount of energy released when the ice melts.
Energy released = mass of ice × heat of fusion
Energy released = 100.0 g × 335 J/g
Energy released = 33500 J
To determine if there is sufficient ice, we need to compare the heat needed to cool the water and the energy released when the ice melts.
If the energy released when the ice melts is more than or equal to the heat needed to cool the water, then there is sufficient ice. Otherwise, there is not enough ice.
In this case:
Energy released = 33500 J
Heat needed = 2510.4 J
Since the energy released (33500 J) is greater than the heat needed (2510.4 J), there is sufficient ice to cool the water to 5.00°C and still have ice remaining.
To summarize, 2510.4 J of heat must be removed from the water to achieve the desired temperature change of cooling from 25.0°C to 5.00°C. There is sufficient ice to cool the water to the desired temperature, with an energy release of 33500 J when the ice melts.
To determine whether the given amount of ice is sufficient to lower the temperature of water to 5.00 degrees Celsius and still have ice remaining, we need to calculate the amount of heat energy required to cool down the water from 25.0 degrees Celsius to 5.00 degrees Celsius.
First, let's find the initial heat energy of the water:
q1 = m1 * c1 * ΔT1
Where:
q1 = heat energy of water
m1 = mass of water
c1 = specific heat capacity of water (4.184 J/g°C)
ΔT1 = temperature change of water (initial temperature - final temperature)
Given:
m1 = 300.0 g
c1 = 4.184 J/g°C
ΔT1 = 25.0°C - 5.0°C = 20.0°C
Substituting the values into the equation:
q1 = (300.0 g) * (4.184 J/g°C) * (20.0°C)
q1 ≈ 25,104 J
Next, let's calculate the heat energy required to convert the ice at 0 degrees Celsius to water at 0 degrees Celsius, known as the heat of fusion:
q2 = m2 * ΔHf
Where:
q2 = heat energy of ice
m2 = mass of ice
ΔHf = heat of fusion of ice (335 J/g)
Given:
m2 = 100.0 g
ΔHf = 335 J/g
Substituting the values into the equation:
q2 = (100.0 g) * (335 J/g)
q2 = 33,500 J
Now, let's calculate the total heat energy required to achieve the desired temperature change:
q_total = q1 + q2
q_total = 25,104 J + 33,500 J
q_total = 58,604 J
The calculated heat energy required to achieve the desired temperature change of the water is approximately 58,604 J.
To check if there is sufficient ice to cool the water, we need to compare the heat energy required (q_total) to the amount of heat energy that can be absorbed by the ice.
The equation to calculate the amount of heat energy that can be absorbed by the ice is:
q_ice = m2 * c_ice * ΔT2
Where:
q_ice = heat energy absorbed by the ice
m2 = mass of ice
c_ice = specific heat capacity of ice (This value is usually negligible compared to water, so we can assume it to be close to 0.)
ΔT2 = temperature change of ice (0°C - final temperature)
Given:
m2 = 100.0 g
c_ice ≈ 0 (Assumed)
ΔT2 = 0°C - 5.0°C = -5.0°C
Substituting the values into the equation:
q_ice = (100.0 g) * 0 * (-5.0°C)
q_ice = 0 J
Since the heat energy that can be absorbed by the ice (q_ice) is 0 J, it means that the ice does not have the capacity to absorb enough heat energy to cool down the water to 5.00 degrees Celsius. Therefore, the given amount of ice is not sufficient to achieve the desired temperature change.