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Chapter 17: Problem 16

You are outside on a hot day, with the air temperature at \(T_{0}\). Your sports drink is at a temperature \(T_{\mathrm{d}}\) in a sealed plastic bottle. There are a few remaining ice cubes in the sports drink, which are at a temperature \(T_{\mathrm{i}}\), but they are melting fast. a) Write an inequality expressing the relationship among the three temperatures. b) Give reasonable values for the three temperatures in degrees Celsius.

Short Answer

Expert verified
Question: On a hot day, a person decides to cool their sports drink using ice cubes. Considering the air temperature, the drink temperature, and the ice temperature, write an inequality expressing the relationship among the three temperatures and provide reasonable values for each temperature in degrees Celsius. Answer: The inequality representing the relationship among the air temperature (T₀), the drink temperature (T_d), and the ice temperature (T_i) is T_i < T_d < T₀. A possible set of temperatures in degrees Celsius could be T_i = 0°C, T_d = 10°C, and T₀ = 30°C.

Step by step solution

01

a) Write an inequality expressing the relationship among the three temperatures.

To find the relationship among the three temperatures, think about the physical situation: the air is hot, the drink is cooler than the air but warmer than the ice, and the ice cubes are melting. Since the ice is melting, it must be at a temperature lower than both the air and the sports drink. Therefore, we can write the inequality as: $$ T_i < T_d < T_0 $$ This means that the ice temperature is less than the drink temperature, which is, in turn, less than the air temperature.
02

b) Give reasonable values for the three temperatures in degrees Celsius.

Now, let's assign reasonable values to each temperature: - Ice temperature, \(T_i\): Since ice is melting, it must be at around its melting point, which is 0°C. - Sports drink temperature, \(T_d\): The drink is not as hot as the air but warmer than the ice cubes. A reasonable temperature could be 10°C; cold enough to still feel refreshing, but not too cold so that the ice would not melt. - Air temperature, \(T_0\): As it is a hot day, a reasonable temperature for the air could be 30°C. So, a possible set of temperatures is: $$ T_i = 0°C ,\, T_d = 10°C ,\, T_0 = 30°C $$

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Most popular questions from this chapter

The Rankine temperature scale is an absolute temperature scale that uses Fahrenheit degrees; that is, temperatures are measured in Fahrenheit degrees, starting at absolute zero. Find the relationships between temperature values on the Rankine scale and those on the Fahrenheit, Kelvin, and Celsius scales.

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