Question

Suppose you are selling apple cider for two dollars a gallon when the temperature is 3.3 degree C. The coefficient of volume expansion of the cider is 280*10^-6(C degree)^-1. How much more money (in pennies) would you make per gallon be refilling the container on a day when the temperature is 32 degrees C? Ignore the expansion of the container. Round your answer to 0.1 penny.

Answer 1

Answer:

1.6 penny

Explanation:

$V_0$ = Original volume = 1 gal (Assumed)

$\Delta T$ = Change in temperature

$\beta$ = Coefficient of volume expansion = $280\times 10^{-6}\ /^{\circ}$

Change in volume is given by

$\Delta_V=\beta V_0\Delta T\\\Rightarrow \Delta_V=280\times 10^{-6}\times 1\times (32-3.3)\\\Rightarrow \Delta_V=0.008036$

New volume would be

$1+0.008036=1.008036\ gal$

The amount of money earned extra would be

$0.008036\times 2=0.016072$

1.6 penny more would be earned if the temperature is 32°C