Which of the following would require more energy to heat it from 10°C
to 20°C?
a. 200 kg of water
b. 200 kg of aluminum
c. 100 kg of steel
How much heat energy is required to raise the temperature of
20 kilograms of water from 0°C to 35°C?
Dhdn
To determine which of the given materials requires more energy to heat from 10°C to 20°C, we need to consider the specific heat capacity of each material.
The specific heat capacity is the amount of energy required to raise the temperature of 1 kilogram of a substance by 1 degree Celsius. The higher the specific heat capacity, the more energy is required to increase the temperature of the material.
To find the specific heat capacity of each material, we can use reference tables or search online.
Let's assume:
Specific heat capacity of water = 4.18 J/g°C (grams per degree Celsius)
Specific heat capacity of aluminum = 0.897 J/g°C
Specific heat capacity of steel = 0.49 J/g°C
Now, let's calculate the energy required to heat each material from 10°C to 20°C:
a. 200 kg of water:
First, convert kg to g: 200 kg * 1000 g/kg = 200,000 g
Energy required = Mass * Specific heat capacity * Change in temperature
= 200,000 g * 4.18 J/g°C * (20°C - 10°C)
= 200,000 g * 4.18 J/g°C * 10°C
= 8,360,000 J
b. 200 kg of aluminum:
Energy required = Mass * Specific heat capacity * Change in temperature
= 200,000 g * 0.897 J/g°C * (20°C - 10°C)
= 200,000 g * 0.897 J/g°C * 10°C
= 1,794,000 J
c. 100 kg of steel:
First, convert kg to g: 100 kg * 1000 g/kg = 100,000 g
Energy required = Mass * Specific heat capacity * Change in temperature
= 100,000 g * 0.49 J/g°C * (20°C - 10°C)
= 100,000 g * 0.49 J/g°C * 10°C
= 490,000 J
Therefore, the material that requires the most energy to heat from 10°C to 20°C is 200 kg of water (8,360,000 J).
Now let's calculate the heat energy required to raise the temperature of 20 kilograms of water from 0°C to 35°C:
Mass of water = 20 kg
Change in temperature = 35°C - 0°C = 35°C
Energy required = Mass * Specific heat capacity * Change in temperature
= 20 kg * 4.18 J/g°C * 35°C
= 2940 J/g°C * 20 kg * 35°C
= 2,058,000 J
Therefore, the heat energy required to raise the temperature of 20 kilograms of water from 0°C to 35°C is 2,058,000 Joules.