Given that electricity is priced at constant 13.5 pence per kWh and central heating oil (kerosine) varies in price between 39 pence and 137 pence per litre. What price does kerosine need to be to make heating domestic hot water cheaper using an immersion heater? Assume oil boiler efficiency to be 80%. Thanks Mike

To determine the price at which kerosene needs to be in order to make heating domestic hot water cheaper using an immersion heater, we need to compare the costs of heating water using electricity and kerosene, taking into account the efficiency of an oil boiler.

Here are the steps to calculate the cost comparison:

1. Convert the electricity price to pence per liter:
Since electricity is priced at 13.5 pence per kWh (kilowatt-hour), we need to convert it to pence per liter. The conversion factor depends on the heat output of the immersion heater. Assuming an average conversion factor of 3.6 kWh per liter of heating oil, we can calculate the electricity price per liter as:

Electricity price per liter = 13.5 pence / (3.6 kWh/liter) = 3.75 pence/liter

2. Calculate the cost of heating water using electricity:
Multiply the electricity price per liter by the amount of electricity required to heat the water to get its cost. Assuming the efficiency of the immersion heater is 100%, the electricity cost to heat the water can be calculated as:

Electricity cost = Electricity price per liter * Volume of water (in liters)

3. Calculate the cost of heating water using kerosene:
Multiply the kerosene price per liter by the amount of kerosene required to heat the water, considering the efficiency of the oil boiler. Since the oil boiler efficiency is given as 80%, the kerosene cost to heat the water can be calculated as:

Kerosene cost = (Kerosene price per liter / 0.8) * Volume of water (in liters)

4. Equate the costs of heating water using electricity and kerosene:
Set the electricity cost equal to the kerosene cost, and solve for the kerosene price per liter:

3.75 pence/liter * Volume of water (in liters) = (Kerosene price per liter / 0.8) * Volume of water (in liters)

Cancel out the Volume of water (in liters) on both sides of the equation,
Multiply both sides by 0.8,
Then solve for the Kerosene price per liter:

Kerosene price per liter = 3.75 pence/liter * 0.8

Kerosene price per liter = 3 pence/liter

Therefore, kerosene needs to be priced at 3 pence per liter or lower to make heating domestic hot water cheaper using an immersion heater, given the given assumptions.