Final answer:
The person will make a profit by selling the vodka at a higher temperature because the increase in volume from the thermal expansion of both ethyl alcohol and water leads to a larger total volume of vodka to sell.
Step-by-step explanation:
The question involves calculating the change in volume of a mixture of ethanol and water when the temperature is increased from -5 °C to 40 °C, to determine if there will be a profit made by selling the vodka at the same price per liter, despite the change in volume due to thermal expansion.
First, we need to determine the change in volume for each component (ethyl alcohol and water) using their respective volume coefficients of thermal expansion. We can then calculate the total change in volume for the 50 liters of vodka, which is a 50-50 mixture of both components.
The volume change for each component is given by the formula: ∆V = αV0∆T, where ∆V is the change in volume, α is the coefficient of volume expansion, V0 is the initial volume, and ∆T is the change in temperature. Since the vodka is sold at the same price per liter, if the volume increases, more liters can be sold, resulting in a profit. If the volume decreases or remains the same, no profit will be made as the selling price hasn't changed.
After carrying out the calculations, it's found that both components will increase in volume, leading to an overall increase in the volume of vodka due to the greater volume coefficient of ethyl alcohol compared to water. This means more liters of vodka to sell at the higher temperature, leading to a profit.