Answer :
To solve the problem, we need to find two things: the calorific value of the fuel and the average energy consumed per day by a family using LPG. Let's break this down step by step.
Calorific Value of the Fuel:
The calorific value of a fuel is the amount of energy produced by the combustion of one kilogram of fuel. It is usually expressed in kilojoules per kilogram (kJ/kg).
We know that burning 1.5 kg of fuel produces 67,500 kJ of energy. To find the calorific value, we can use the formula:
[tex]\text{Calorific Value} = \frac{\text{Total Energy Produced}}{\text{Mass of Fuel}} = \frac{67,500 \text{ kJ}}{1.5 \text{ kg}}[/tex]
Performing the division gives:
[tex]\text{Calorific Value} = 45,000 \text{ kJ/kg}[/tex]
Average Energy Consumed Per Day Using LPG:
We know the family consumes 12 kg of LPG over 30 days, and the calorific value of LPG is given as 50,000 kJ/kg.
First, let's calculate the total energy consumed in 30 days:
[tex]\text{Total Energy Consumed} = \text{Calorific Value of LPG} \times \text{Mass of LPG Used} = 50,000 \text{ kJ/kg} \times 12 \text{ kg}[/tex]
[tex]\text{Total Energy Consumed} = 600,000 \text{ kJ}[/tex]
Now, to find the average energy consumed per day, divide the total energy by the number of days:
[tex]\text{Average Energy Per Day} = \frac{\text{Total Energy Consumed}}{\text{Number of Days}} = \frac{600,000 \text{ kJ}}{30}[/tex]
Performing the division gives:
[tex]\text{Average Energy Per Day} = 20,000 \text{ kJ/day}[/tex]
In summary, the calorific value of the fuel is 45,000 kJ/kg, and the average energy consumed by the family per day is 20,000 kJ.
