Volume Expansion: Find Petrol Overflow After Temp Change

[Pao44445]

Homework Statement

a steel tank is 70 litres,full of petrol. If a temperature is change from 20^o C to 35^o, find the increased volume of petrol that overflows

(β_steel = 950 x 10^-6 )
β_petrol = 36 x 10^-6 )

Homework Equations

Δv=βv₀ΔT

The Attempt at a Solution

I know that both the steel tank and petrol will be increased by the heat and my equation is

change in volume of petrol - change in volume of steel = volume of petrol that overflows
Δv_petrol - Δv_steel = v_f

and I got stuck with the volume of the tank :/

 

[kuruman]

I think that you are expected to assume that the tank is full to the brim. Otherwise, you will not be able to do the problem.

 

[Pao44445]

I think that you are expected to assume that the tank is full to the brim. Otherwise, you will not be able to do the problem.

yes, in that case

 

[gneill]

(β_steel = 950 x 10^-6 )
β_petrol = 36 x 10^-6 )

I think you may have swapped the β values. If there's to be an overflow, shouldn't the oil volume expand more than the steel volume for the same change in temperature?

 

[CWatters]

+1 google suggest the beta values have been swapped. I found 33 for iron and 700ish for various oils.

 

[Pao44445]

I think you may have swapped the β values. If there's to be an overflow, shouldn't the oil volume expand more than the steel volume for the same change in temperature?

Oops, yes my mistake ( I can't edit on my phone right now)

I asked my friend, she said the volume of the tank is the same as petrol but why? Or we assume that wall the tank is very thin?

 

[Chestermiller]

Oops, yes my mistake ( I can't edit on my phone right now)

I asked my friend, she said the volume of the tank is the same as petrol but why? Or we assume that wall the tank is very thin?

Why would the wall thickness of the tank be a factor?

 

[gneill]

I asked my friend, she said the volume of the tank is the same as petrol but why? Or we assume that wall the tank is very thin?

You can think of it as the tank's fluid capacity (the volume of its interior space). You can imagine the walls of the tank being as thick or thin as you wish so long as its initial capacity matches the given amount of oil.

 

[kuruman]

I asked my friend, she said the volume of the tank is the same as petrol but why? Or we assume that wall the tank is very thin?

Wall thickness doesn't matter. Say the inside volume of the tank which defines its capacity is V₀. When the temperature changes, the new volume is V_new = V₀ + βV₀ΔT = V₀(1+βΔT). You can view this as saying that thermal expansion is like enlarging a photograph of the tank by a factor of (1+βΔT). All relative proportions, e.g. the ratio of wall thickness to the tank's height, remain the same. Initially, the inside volume of the tank and the volume of the petrol are the same. When the temperature rises, the "photograph" of the petrol is "enlarged" by a larger factor than the "photograph" of the tank's inside volume. As long as you keep the tank's capacity (or inside volume) the same, you can add as much wall thickness to the outside of the tank and the answer will not change.