9702_s22_qp_13 Question 16

A technical article about diesel engines expresses the energy available from diesel fuel both as 41.8 MJ kg^–1 and as 34.9 GJ m^–3. 

What is the density of diesel fuel? 

A 8.35 x 10² kg m^–3 

B 1.20 x 10³ kg m^–3 

C 8.35 x 10⁵ kg m^–3 

D 1.20 x 10⁶ kg m^–3

ANSWER: 

The Physics behind the answer:

• Density is mass per unit volume.

ρ = m / V

• The information given in the problem are
• energy per unit mass, 

E / m

• energy per unit volume, 

E / V

• To determine the density, you need to find the volume that gives equal amount of energy per 1 kg mass [or vice-versa].
• Energy for every kilogram is 

41.8 MJ kg^–1.

• By ratio and proportion, the same amount of energy for every m³ is

34.9 GJ / 1 m³= 41.8 MJ / V

V= 1.20 x 10^–3 m³

• Density therefore is

ρ = m / V

ρ = 1 kg / 1.20 x 10^–3 m³

ρ = 835 kg m^–3 

[or option A]