Please show each step: If you want to heat 100 kg of water at 20 ° C for your bath, calculate the amount of heat in water. Then it shows that this is equivalent to 8360 kilojoules.
To calculate the amount of heat in water, we need to use the specific heat capacity of water and the equation for calculating heat energy.
Step 1: Find the specific heat capacity of water.
The specific heat capacity of water is approximately 4.186 joules/gram °C. This means that 1 gram of water requires 4.186 joules of energy to raise its temperature by 1 °C.
Step 2: Convert the mass of water from kilograms to grams.
Since the specific heat capacity is given in terms of grams, we need to convert the mass of water from kilograms to grams. To do that, we multiply the mass in kilograms by 1000 (since there are 1000 grams in a kilogram).
Given mass of water = 100 kg
Converted mass of water = 100 kg × 1000 g/kg = 100,000 g
Step 3: Calculate the change in temperature.
The change in temperature is the difference between the final temperature and the initial temperature. In this case, the final temperature is the desired bath temperature, which is 20 °C. The initial temperature is not provided, so we assume it is 0 °C since we are heating the water from room temperature.
Change in temperature = Final temperature - Initial temperature
Change in temperature = 20 °C - 0 °C = 20 °C
Step 4: Calculate the amount of heat using the equation.
The equation to calculate heat energy is:
Heat energy = mass × specific heat capacity × change in temperature
Plugging in the values:
Heat energy = 100,000 g × 4.186 J/g°C × 20 °C
Step 5: Convert the heat energy to kilojoules.
The result from the previous step is the heat energy in joules. To convert it to kilojoules, we divide it by 1000.
Converted heat energy = (100,000 g × 4.186 J/g°C × 20 °C) / 1000
Simplifying the equation:
Converted heat energy = 83,720 J / 1000
Final Answer: The amount of heat required to heat 100 kg of water at 20 °C is 83,720 J, which is equivalent to 83.72 kilojoules (rounded to two decimal places).