Archimedes decides to take a warm bath. If 1 calorie equals 4.187 Joules,
and the heat of fusion of ice/water is 334 J/gram, calculate the number of calories it takes to liquefy a solid block of ice of mass 100 kg at 0°C.
Use scientific notation.
Q=λm=334 000 J/kg •100 kg =33400000 J=3.34•10^7J=7977452.9 cal=
7.98 •10^6 cal
To calculate the number of calories it takes to liquefy a solid block of ice, we need to follow these steps:
Step 1: Determine the heat of fusion of ice.
Given: Heat of fusion of ice/water = 334 J/gram
Step 2: Calculate the total heat required to melt the ice.
Total heat = mass × heat of fusion
Given: Mass of ice = 100 kg
Since the heat of fusion is given in joules per gram, we need to convert the mass of the ice from kilograms to grams.
Mass of ice in grams = Mass of ice in kilograms × 1000
Mass of ice in grams = 100 kg × 1000
Mass of ice in grams = 100,000 g
Total heat = (Mass of ice in grams) × (Heat of fusion)
Total heat = 100,000 g × 334 J/g
Step 3: Convert the total heat from joules to calories.
Since 1 calorie is equal to 4.187 joules, we can convert joules to calories by dividing the total heat by the conversion factor.
Total heat in calories = Total heat in joules / Conversion factor
Total heat in calories = (100,000 g × 334 J/g) / 4.187 J/calorie
Now we can calculate the total heat required to liquefy the ice block in calories. Let's perform the calculation:
Total heat in calories = (100,000 × 334) / 4.187
Total heat in calories = 8,002,394.825646003
Therefore, it takes approximately 8,002,395 calories (in scientific notation) to liquefy a solid block of ice with a mass of 100 kg at 0°C.