Question

On a hot day in Jaipur, an oil trucker loaded 40 kL (kilolitres) of diesel fuel. On his way to Shimla, he encounters a temperature drop of 20∘C, where he stopped and delivered the entire load. How many litres did he deliver? The γ for diesel is 9.50 × 10−4/∘C and α for his steel truck is 11 × 10−6/∘C. If you find that the volume has decreased, think about who is paying for the "missing” diesel.

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Solution

The correct option is **A**

39,240 L

Since it got colder going from Jaipur to Shimla by 20∘C, ΔT = -20∘C.

The volume of diesel that he delivers at Shimla-

V′ = V(1+γΔT)

⇒ V′ = 40,000[1+9.5×10−4 × (−20)] litres

⇒ V′ = 39,240 litres.

Which means, he delivered (40,000 - 39,240) = 760 litres less diesel at Shimla. This is a real life problem. How do you think we circumvent this issue? When it comes to such large deliveries, the amount of fuel is kept track of by measuring the mass/weight instead of volume, of course! What about petrol pumps? You might be aware that we always pay for the volume of petrol. Will this be an issue there? To avoid this, petrol and diesel are priced slightly differently in different states, assuming there is not much of a temperature variation within a state (although, there are other reasons too).

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