When ice melts, it absorbs 0.33 kJ/g. How much ice is required to cool a 11.0oz drink from 76F to 39F, if the heat capacity of the drink is 4.18J/gC ? (Assume that the heat transfer is 100% efficient.)
I got 11 g, but I guess that's wrong...
To calculate the amount of ice required to cool the drink, we need to use the equation:
Q = mcΔT
Where:
Q is the heat absorbed by the drink (in joules)
m is the mass of the drink (in grams)
c is the specific heat capacity of the drink (in J/gC)
ΔT is the change in temperature of the drink (in Celsius)
First, let's convert the given values to the appropriate units:
11.0 oz = 311 grams (1 ounce = 28.35 grams)
76°F = 24°C (using the conversion formula °C = (°F - 32) / 1.8)
39°F = 4°C
Now let's calculate the heat absorbed by the drink:
Q = (311 g) * (4.18 J/gC) * (4°C - 24°C)
Q = -24879.6 J (the negative sign indicates that heat is being removed from the drink)
Now, let's convert the heat value to kilojoules:
Q = -24.9 kJ (since 1 J = 0.001 kJ)
Since 1 gram of ice absorbs 0.33 kJ of heat, we can calculate the mass of ice required:
mass of ice = Q / heat absorbed per gram of ice
mass of ice = -24.9 kJ / 0.33 kJ/g
mass of ice ≈ -75.4 g
The negative sign indicates that the ice has to absorb this amount of heat. In reality, we cannot have a negative mass, so we can take the absolute value:
mass of ice ≈ 75.4 g
Therefore, approximately 75.4 grams of ice is required to cool the drink from 76°F to 39°F.
To solve this problem, you need to calculate the amount of heat required to cool the drink from 76°F to 39°F, and then use that to determine the mass of ice needed to absorb that amount of heat.
First, let's convert the temperature from Fahrenheit to Celsius, since the heat capacity is given in J/g°C, which is the metric unit system.
(76°F - 32) × 5/9 = 24°C
(39°F - 32) × 5/9 = 4°C
Next, calculate the amount of heat required to change the temperature of the drink using the formula:
Heat = mass × heat capacity × temperature change
Since the heat capacity is given in J/g°C, we need to convert ounces to grams, and kJ to J.
1 oz = 28.35 g
1 kJ = 1000 J
So, the heat required can be calculated as:
Heat = (11.0 oz) × (28.35 g/oz) × (4.18 J/g°C) × (24°C - 4°C)
Simplifying the equation:
Heat = (11.0) × (28.35) × (4.18) × (20)
You should get the heat value in Joules.
Now, let's calculate the mass of ice needed to absorb this heat.
Since ice absorbs 0.33 kJ/g, we can calculate the mass using the formula:
Mass = Heat / heat of fusion
Here, we need to convert heat of fusion from kJ/g to J/g:
1 kJ/g = 1000 J/g
So, the mass of ice can be calculated as:
Mass = Heat / (0.33 kJ/g × 1000 J/kJ)
Simplifying the equation:
Mass = Heat / 330 J/g
Substituting the value of heat, you can calculate the mass.
Please note that the calculation provided here is a guide to help you solve the problem. Make sure to double-check the units and perform the calculations accurately to obtain the correct answer.