Calculate the total heat content of 10 kg of ice at -23°C. (Hint: absolute zero is -273°C.)
Be mindful of significant figure rules for both multiplication and addition.
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Well, I must say, this question is heating things up! Let's get started with some calculations.
To calculate the total heat content, we need to take several things into account. First, we need to determine the heat content of the ice at -23°C. Since ice is at its freezing point at 0°C, the temperature difference is -23°C - 0°C = -23°C.
Now, we also need to account for the heat involved in melting the ice. The heat required to melt ice at its melting point is 334 kJ/kg. So, the heat content of 10 kg of ice at -23°C would be:
Heat content = (temperature difference × specific heat capacity) + (mass of ice × heat of fusion)
Using the specific heat capacity of ice (2.09 J/g°C), we can convert it to kJ/kg°C by multiplying it by the mass of 1 kg (1000 g).
Temperature difference = -23°C - 0°C = -23°C
Specific heat capacity of ice = 2.09 J/g°C × 1000 g/kg = 2090 J/kg°C (rounded to 3 significant figures)
Mass of ice = 10 kg
Heat of fusion = 334 kJ/kg
Now let's plug in these values:
Heat content = (-23°C × 2090 J/kg°C) + (10 kg × 334 kJ/kg)
Calculating this, we get:
Heat content = -47770 J + 3340 kJ
Finally, let's convert the units:
Heat content = -47770 J + 3340 kJ
Heat content = -47770 J + 3.34 MJ
Heat content = -47.77 kJ + 3.34 MJ (rounded to 3 significant figures)
Drum roll, please...
The total heat content of 10 kg of ice at -23°C is approximately 3.29 MJ (rounded to 3 significant figures).
Hope you got warmed up by these calculations!
To calculate the total heat content of the ice, we need to consider two steps:
1. Determine the heat required to raise the ice from -23°C to 0°C.
2. Determine the heat required to melt the ice at 0°C.
Step 1: Determine the heat required to raise the ice from -23°C to 0°C.
The specific heat capacity of ice is 2.09 J/g°C. We will convert the mass of ice from kg to grams.
Mass of ice = 10 kg = 10,000 g
Temperature change = 0°C - (-23°C) = 23°C
Using the equation Q = m * c * ΔT, where Q is the heat required, m is the mass, c is the specific heat capacity, and ΔT is the temperature change, we can calculate the heat required to raise the ice:
Q1 = 10,000 g * 2.09 J/g°C * 23°C
Q1 ≈ 480,700 J
Step 2: Determine the heat required to melt the ice at 0°C.
The heat of fusion for ice is 334 J/g.
Using the equation Q = m * ΔHf, where Q is the heat required, m is the mass, and ΔHf is the heat of fusion, we can calculate the heat required to melt the ice:
Q2 = 10,000 g * 334 J/g
Q2 = 3,340,000 J
Now, we can calculate the total heat content by adding the heat required in step 1 and step 2:
Total heat content = Q1 + Q2
Total heat content ≈ 480,700 J + 3,340,000 J
Total heat content ≈ 3,820,700 J
Therefore, the total heat content of 10 kg of ice at -23°C is approximately 3,820,700 J.
To calculate the total heat content of ice at -23°C, we need to consider two factors: the heat required to raise the temperature from -273°C to 0°C (the melting point of ice) and the heat required to raise the temperature from 0°C to -23°C.
Let's break down the calculation step by step:
Step 1: Calculate the heat required to raise the temperature from -273°C to 0°C.
The specific heat capacity (c) of ice is 2.09 J/g°C. First, we need to convert 10 kg of ice to grams:
10 kg * 1000 g/kg = 10,000 g
The temperature change is 0°C - (-273°C) = 273°C
The heat required is calculated using the formula:
Q = mcΔT
Q = (10,000 g) * (2.09 J/g°C) * (273°C)
Q = 5,766,300 J (or 5.77 x 10^6 J)
Step 2: Calculate the heat required to raise the temperature from 0°C to -23°C.
The specific heat capacity (c) of ice is the same, 2.09 J/g°C.
The temperature change is (-23°C) - 0°C = -23°C
The heat required is calculated using the formula:
Q = mcΔT
Q = (10,000 g) * (2.09 J/g°C) * (-23°C)
Q = -479,300 J (or -4.79 x 10^5 J)
Step 3: Calculate the total heat content.
To find the total heat content, we need to add the heat required in step 1 and step 2 together:
Total heat content = (5,766,300 J) + (-479,300 J)
Total heat content = 5,287,000 J (or 5.29 x 10^6 J)
Therefore, the total heat content of 10 kg of ice at -23°C is 5,287,000 J (or 5.29 x 10^6 J).
10 kg * 2.108 kJ/kg-K * (-23 + 273)K
= 5270 k J
= 5,270,000 J