Ethanol has a density of 800 kgm3 at 0c and an average...

Ethanol has a density of 800 kg/m³ at 0°C and an average coefficient of volume expansion of 1.09 × 10⁻³ (°C)⁻¹. Imagine you are pumping ethanol into a vehicle's fuel tank. How many extra kilograms of ethanol would you receive if you bought 11.0 gallons of ethanol at 0°C rather than at 19.2°C from a pump that is not temperature compensated? Note that 1 gallon is 3.7854 × 10⁻³ m³. (Include the sign of the value in your answer.)

Transcript

00:01 Hello students in this question we are given the density of ethanol that is row which is equal to 800 kg per meter cube and we are given the average coefficient of volume expansion here average coefficient of volume expansion which is equal to 1 .09 multiplied 10 to the power minus 3 per degree celsius and we are given that one gallon is equal to 3 .7854 multiplied 10 to the per minus 3 meter cube and we have bought 11 gallons at 0 degrees celsius so it means 11 gallons will be 11 multiplied with 3 .78 54.

01:06 Multiply it 10 to the power minus 3 so this comes out to be here the volume comes out to be 0 .41 6394 meter cube this is the volume now the temperature at it is what is given to us here which is t 1 which is 0 degrees celsius and rather than at t 2 which is 90 2 degrees celsius now we know that at high temperature the volume increases by a factor so the volume v so the factor is equal to or we can write it as here now the factor by which the volume increases is equal to 1 plus alpha multiply by delta t is equal to this is equal to 1 plus 0 .001 .09 multiplied by this is 19 .2 delta.

02:16 So from here we get 1 .020928.

02:20 So the density at 0 degrees celsius is 800 kg per meter cube.

02:29 Now density at 19 .2 degrees celsius is equal to this is 800 over the factor which is 1 .02098 so this comes out to be 783 .60 kg per meter cube so now if we add 0 degrees celsius if we find out the mass so mass is density multiplied by volume so density is 800 minus multiplied by volume volume is 0.

03:04 4 here the volume is 0 .4164 here it is 0 .0 .0 .041 so it is 0 .0 .0 416394 so this comes out to be so 33 .3 .3 kj and and add 19 .2 degrees celsius if we find out the mass which is density multiplied by volume so density is 783 .60 multiply by volume will be 0 .0 4163 .94 so this comes out to be this is here 302 .628 628 628 6 to 3 3 3 kg now now the difference in mass, difference in mass will be equal to 33 .31152 minus 32 .62863...

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