On a hot day at Chennai, an oil tanker was loaded with 40000 litres of diesel fuel. The tanker was then driven to Ooty where the temperature was 20 K lower than in Chennai and the entire load was delivered at Ooty. If the coefficient of volume expansion for diesel fuel is 1 × 10-3/K, the quantity of diesel delivered at Ooty was

Concept:

Coefficient of volume expansion:

\(β = \frac{1}{V} × \frac{{{\rm{Δ }}V}}{{{\rm{Δ }}T}}\)

where,

V = Initial Volume

ΔV = Change in volume, i.e. final volume - initial volume

ΔT = Change in Temperature, i.e. Final temperature - Initial temperature

Calculation:

Given:

β = 1 × 10-3 /K, V = 40000 litres

Let's assume, the temperature at Chennai i.e. initial temperature = T1, the temperature at Otty i.e. final temperature = T₂

Also we have, T₂ = T₁ - 20

ΔT = T2 - T1

ΔT = -20 K

Also, \(β = \frac{1}{V} × \frac{{{\rm{Δ }}V}}{{{\rm{Δ }}T}}\)

So, ΔV = β × V × ΔT

ΔV = 1 × 10-3 × 40000 × (-20)

ΔV = -800 litres

Since, change in volume = final volume - initial volume

Final Volume = 40000 + (-800)

Final Volume = 39200 liters

Hence the quantity of diesel delivered at Ooty was 39200 liters.