Coefficient of volumetric expansion of gasoline at different temperatures

[Doshke]

Homework Statement:

Task: The weight of gasoline at 0 ° C is 88N. At 60 °C the weight of the same volume of gasoline is 83N. What is the coefficient of volume expansion of gasoline?

Relevant Equations:

in the picture below are

I tried to solve the task in different ways, I had different ideas but none of them led me to the correct solution.

I would be grateful if someone would explain at least the initial part of the task to me.

True answer: 10^-3K^-1

 

[haruspex]

Where does the equation $\frac{m_0}{m_1}=1.06$ come from? There is no change to the mass.

 

[kuruman]

You have the right equation relating the final volume to the initial volume, $V_f=V_i(1+\beta \Delta T).$ I think the easiest way to proceed from here is to find $V_f$ assuming constant mass. Then $\rho_i V_i=\rho_f V_f.$ Perhaps you can continue from here on your own.

 

[kuruman]

Where does the equation $\frac{m_0}{m_1}=1.06$ come from? There is no change to the mass.

The problem doesn't say anything to this effect, but it is instinctive to think that the gasoline is contained in a tank and some of the fluid spilling over when the temperature rises. (That was my impulsive original thought.) I have seen a similar problem in which both gasoline and tank expand and one has to find the amount of spilled gasoline.

 

[haruspex]

The problem doesn't say anything to this effect, but it is instinctive to think that the gasoline is contained in a tank and some of the fluid spilling over when the temperature rises. (That was my impulsive original thought.) I have seen a similar problem in which both gasoline and tank expand and one has to find the amount of spilled gasoline.

Yes, I should have been clearer.
@Doshke's algebra started by taking mass constant and computing the change in volume. That would have worked, but it then switched to taking it as a change in mass. That also would work, but unfortunately the two approaches got interwoven and cancelled, leading to the loss of the 1.06 factor.

 

[Doshke]

You have the right equation relating the final volume to the initial volume, $V_f=V_i(1+\beta \Delta T).$ I think the easiest way to proceed from here is to find $V_f$ assuming constant mass. Then $\rho_i V_i=\rho_f V_f.$ Perhaps you can continue from here on your own.

Thank you for your help @haruspex @kuruman I managed to do the task.
This observation saved me
$\rho_i V_i=\rho_f V_f.$