if you wished to warm 100 kg of water by 15 degrees celsius for your bath, how much heat would be required? (give your answer in calories and joules)
Q (heat) = M*C*(delta T)
= 100,000 g * 1.00 cal/g C * 15 deg
= ? cal
To get the answer in Joules, multiply the number of calories by 4.18
150000
To calculate the amount of heat required to warm water, you can use the specific heat capacity of water and the formula:
Q = m * c * ΔT
Where:
Q is the heat required
m is the mass of water
c is the specific heat capacity of water
ΔT is the change in temperature
Given:
m = 100 kg (mass of water)
c = 1 calorie/gram·degree Celsius (specific heat capacity of water)
ΔT = 15 degrees Celsius (change in temperature)
To convert the mass from kilograms to grams:
m = 100 kg * 1000 g/kg = 100,000 g
Calculating the heat required in calories:
Q = (100,000 g) * (1 calorie/gram·degree Celsius) * (15 degrees Celsius)
Q = 1,500,000 calories
To convert calories to joules:
1 calorie = 4.184 joules
Calculating the heat required in joules:
Q = (1,500,000 calories) * (4.184 joules/calorie)
Q = 6,276,000 joules
So, the heat required to warm 100 kg of water by 15 degrees Celsius for your bath is 1,500,000 calories or 6,276,000 joules.
To determine the amount of heat required to raise the temperature of water by a certain amount, we need to use the specific heat capacity of water. The specific heat capacity of water is approximately 4.186 Joules per gram per degree Celsius or 1 calorie per gram per degree Celsius.
Step 1: Convert the mass into grams:
100 kg = 100,000 grams
Step 2: Calculate the heat energy required using the specific heat capacity:
Heat energy (in Joules) = Mass (in grams) × Specific Heat Capacity (J/g°C) × Temperature Change (in °C)
Heat energy (in calories) = Mass (in grams) × Specific Heat Capacity (cal/g°C) × Temperature Change (in °C)
For Joules:
Heat energy (in J) = 100,000 g × 4.186 J/g°C × 15 °C
For calories (1 calorie = 4.186 Joules):
Heat energy (in cal) = 100,000 g × 1 cal/g°C × 15 °C
Calculating the heat energy,
For Joules:
Heat energy = 6,279,000 J
For calories:
Heat energy = 1,500,000 cal
Therefore, to warm 100 kg of water by 15 degrees Celsius, approximately 6,279,000 Joules or 1,500,000 calories of heat energy are required.