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

1.6 penny

Step-by-step explanation:

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

`\Delta T` = Change in temperature

`\beta` = Coefficient of volume expansion =
`280* 10^(-6)\ /^(\circ)`

Change in volume is given by

`\Delta_V=\beta V_0\Delta T\\\Rightarrow \Delta_V=280* 10^(-6)* 1* (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* 2=0.016072\ \$`

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