Calculating the mass and price of LPG needed to heat water

[PraAnan]

Hello everyone,

Homework Statement
How many kilograms of lpg will you use if you heat 5 litres of water from 20C to 90C everyday for 30 days and how much will that cost if a 12.5kg cylinder is 1750 Rupees

The attempt at a solution
To heat 1 liter of water by 1C requires 4.18kJ so you then multiply this by 70 (the temperature difference) and then by 150 (the total amount of water) which gives 43,890kJ.

A kg of lpg =49,000kJ
So at 100% efficiency you will need 0.9kg of gas.

This is the part I'm not sure about, the efficiency of gas stoves.
I read that a typical stove is 50-60% efficient so at 50% efficiency you would need 1.8kg of gas which at a price of 140 Rupees per kg will come to 252 Rupees.

Is this correct or am I missing something obvious?

Thanks for reading

 

[mfb]

If there is no efficiency given anywhere I would assume 100% and comment that this too optimistic.

 

[PraAnan]

If there is no efficiency given anywhere I would assume 100% and comment that this too optimistic.

Thanks for the reply.

There is nothing mentioned about efficiency but I did write it because a part of the question which I didn't write as I thought it wasn't that important at the time (I translated it from our local language) actually says: if you heat 5 litres of water from 20C to 90C everyday using a gas cooker for 30 days.

I won't lose anything by writing the 100% value as well as the value after efficiency has been taken into account.

Apart from that though, I take it that the rest of my work was correct? and is the 50% number actually accurate? (I have since come across a post about a person testing the time it takes to boil water with an induction and gas cooker and they worked out that the efficiency of the gas cooker was 32%)

 

[CWatters]

Looks ok to me.

When you burn LPG the main products are CO2 and water vapour both of which are hot. The efficiency of a pan of water on a gas stove is poor because these products escapes around the sides of the pan into the air without giving up much heat to the pan.

Some types of home heating system are much more efficient. In the UK most new gas water heaters have a condenser which recovers the latent heat from the water vapour. These can achieve efficiencies of over 90%.

If you use an electric heater with the element immersed in the water almost of the heat goes into the water and the efficiency can be close to 100% (if you ignore losses through the walls of the container).

 

[PraAnan]

Thanks for the help. : )

 

[Shan119]

Hello everyone,

Homework Statement
How many kilograms of lpg will you use if you heat 5 litres of water from 20C to 90C everyday for 30 days and how much will that cost if a 12.5kg cylinder is 1750 Rupees

The attempt at a solution
To heat 1 liter of water by 1C requires 4.18kJ so you then multiply this by 70 (the temperature difference) and then by 150 (the total amount of water) which gives 43,890kJ.

A kg of lpg =49,000kJ
So at 100% efficiency you will need 0.9kg of gas.

This is the part I'm not sure about, the efficiency of gas stoves.
I read that a typical stove is 50-60% efficient so at 50% efficiency you would need 1.8kg of gas which at a price of 140 Rupees per kg will come to 252 Rupees.

Is this correct or am I missing something obvious?

Thanks for reading

What is 150 (total amount of water )? Isnt the formulae is m*Change in temperature*specific heat req? How come is the mass of 1 liter is converted into 150 ??

 

[mfb]

5 liters per day for 30 days, i.e. 150 liters in total.

This thread is from 2019 by the way.