Physics 6 Tutorial 13 - Fuel Cells

This tutorial is for students of the Welsh Board and Eduqas


Fuels for Vehicles

Hydrogen as a Fuel

Fuel Cells

Fuel Cells in Cars


Fuels for Vehicles

Internal combustion engines can be run on fuels other than petrol or diesel.  Will this reduce emissions like carbon dioxide and nitrogen oxides? 


Some vehicles have been converted to run on liquefied petroleum gas (LPG).  In static installations, methane is produced by biogas digesters and fed to a stationary engine and burned there to produce energy.  The same is done with the methane produced in land-fill sites.  In the Second World War, buses and lorries were converted to run on carbon monoxide from the town gas supply.  These carried distinctive large bags of gas on their roofs.


The calorific value (energy per unit mass) of methane is slightly greater than that of petrol or diesel:



Calorific Value / MJ kg-1

Density / kg m-3

















Question 1

If the calorific values of both petrol and diesel are both the same, why does a petrol car burn more fuel (for example a petrol car might burn 6 litres per 100 km, while the equivalent diesel car burns 5 litres per 100 km)?



Perhaps fuel should be sold by the kilogram, and fuel consumption be measure in kilograms per 100 km.


Question 2

Why are petrol and diesel the most common fuels used in vehicles, rather than the gases?



Apart from hydrogen, the fuels above are carbon based, which means that carbon dioxide is emitted from the vehicles.  Also nitrogen oxides (NOx) are produced in the conditions of high temperature and pressure in the cylinders.



Hydrogen as a Fuel

Data from the table above suggest that hydrogen would make an excellent fuel for an internal combustion engine.  It has nearly three times the calorific value of diesel.  So why isn't it used as a car fuel?  It also emits water as an exhaust.

Question 3

A car petrol tank has a capacity of 50 litres.  Use data from the table above to answer the questions.

(a)  Show that the mass of petrol is about 38 kg.

(b) 1 mole (6.0 1023 particles) has a mass of 2.0 10-3 kg.  Calculate how many moles there are in 1 kg of hydrogen.

(c)  Calculate the number of kilograms of hydrogen that would give the same range as the 50 litre tank of petrol.

(d) How many moles is this?

(e) 1 mol of any gas occupies 0.024 m3 at room temperature and pressure.  What is the volume taken by the number of moles you worked out in part (d).

(f) Show that the pressure in the fuel tank is about 3000 atmospheres (atm).



Your answer to the question above should tell you that very high pressures would be needed in the fuel tank of a hydrogen powered vehicle to give it a reasonable range.  A 50-litre tank that will hold hydrogen at that intense pressure would be very heavy indeed with thick stainless steel walls.  It would have a mass that was a significant fraction of the car's mass.


Hydrogen powered vehicles with an internal combustion engine are limited.  Hydrogen filling stations are very few.  Additionally the heat of combustion and pressure in the cylinders will also give rise to nitrogen oxides.  Therefore our dream of a zero-emissions vehicle is as far away as before.  Or is it?



Fuel Cells

One problem with internal combustion engines is that their efficiency is quite low, even if it has improved over recent years.  An electric motor is more efficient.  How do we convert hydrogen to electricity.  We produce hydrogen by passing electricity through an electrolyte.  Can we reverse the process to get electricity back?


The answer is a fuel cell.  It takes in hydrogen as a fuel and its waste is water.  The diagram below shows the idea:



Hydrogen gas (H2) passes into the cell on the left hand side of the fuel cell.  The hydrogen molecules hit the anode, which is made from platinum, a catalyst.  The hydrogen molecules split into hydrogen ions and electrons:



The electrolyte allows protons to cross it, but is contained by a polymer membrane that is impermeable to electrons.  The electrons are left on the anode.  The excess of electrons makes the anode negative.


On the right-hand side oxygen comes in.  The oxygen atoms hit the cathode which is made from nickel (also a catalyst), which facilitates the combination of the oxygen atoms with the hydrogen ions:


The electrons have come through the external circuit, which passes through the load.  In a car, this would be a motor.  The water is given off as steam, as the reaction occurs at a temperature of about 130 oC.


The voltage of such a cell is about 0.7 V.  A car traction motor operates at a typical voltage of 350 V.  So the hydrogen cells have to be placed in series to make a high enough voltage.


Question 4

How many fuel cells are needed in series to make a voltage of 350 V?



A typical current from a fuel cell is about 0.8 A (800 mA).  To provide the currents needed in a typical electric car, the cells would need to be set up in parallel arrays.


Question 5

A particular car has a traction motor rated at a maximum power of 75 kW.

(a) Calculate the current needed.

(b) How many parallel arrays would be needed to provide this current?

(c) Use your answer to question 4 to work out the total number of fuel cells needed.




Fuel Cells in Cars

To make a viable unit to power a car, a very large number of individual fuel cells are needed.  In these examples a DC motor was used as the model.  In modern electric cars, the motors are 3-phase AC motors which have to have inverters to control them


There are many advantages to using fuel cells including:


There are disadvantages:


Question 6


An electric car is travelling along a straight and level road at a constant speed of 100 km h-1.  It draws a current of 200 A from a hydrogen fuel cell.  The current is produced by electrons from the anode.


(a)  Write down an equation that shows how electrons are produced from hydrogen gas.

(b)  Work out how many electrons are taken every second.  (Electronic charge = 1.60 10-19 C)

(c)  How long does it take for the car to use 2.0 g of hydrogen gas (H2)?

(d)  How far will the car travel at this speed?

(e)  State the assumption made in this calculation, and discuss whether the car would travel this far on 2.0 g of H2.  Give an estimate of the true distance the car would travel.