Finding Temperature of Hot Sandwich: Equation & Answers

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In summary, the equation T(t) = 63(0.5)^\frac{t}{10} + 19 models the temperature of a hot sandwich left to cool on a kitchen counter. To find the temperature, we substitute the time t in minutes into the equation and evaluate. For part a, the temperature of the sandwich when recording began would be T(0) = 63(0.5)^\frac{0}{10} + 19 = 64 degrees Celsius. For part b, after 20 minutes, the temperature would be T(20) = 63(0.5)^\frac{20}{10} + 19 = 48 degrees Celsius.
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9) A student records the internal temperature of a hot sandwich that has been left to cool on a kitchen counter. The room temperature is 19 degrees Celsius. An equation that models this situation is \(\displaystyle T(t) = 63(0.5)^\frac{t}{10} + 19\) where \(\displaystyle T\) is the temperature in degrees Celsius and \(\displaystyle t\) is the time in minutes.

a) What was the temperature of the sandwich when she began to record its temperature?
b) Determine the temperature of the sandwich after 20 min.I don't really understand what to do..help would be appreciated. Thanks!
 
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The equation you are given tells you the temperature of the sandwich at time $t$. So, you need to substitute for $t$ and then evaluate the resulting expression on the right side of the equation. What is the value of $t$ for part a)? And for part b)?
 

FAQ: Finding Temperature of Hot Sandwich: Equation & Answers

1. How do you find the temperature of a hot sandwich?

To find the temperature of a hot sandwich, you can use the equation Q = mcΔT. This equation takes into account the mass of the sandwich (m), the specific heat capacity of the sandwich (c), and the change in temperature (ΔT). By plugging in these values, you can calculate the temperature of the hot sandwich.

2. What is the specific heat capacity of a hot sandwich?

The specific heat capacity of a hot sandwich can vary depending on the type of sandwich and its ingredients. Generally, foods with higher water content have a higher specific heat capacity, so hot sandwiches with a lot of toppings or condiments may have a higher specific heat capacity. It is best to look up the specific heat capacity of the individual ingredients and calculate an average for a more accurate result.

3. Can you use a thermometer to find the temperature of a hot sandwich?

Yes, a thermometer can be used to find the temperature of a hot sandwich. However, this method may not be as accurate as using the Q = mcΔT equation since the thermometer may not be able to reach the center of the sandwich where the temperature may be different than the outer layers.

4. How does the type of bread affect the temperature of a hot sandwich?

The type of bread used in a hot sandwich can affect its temperature due to its specific heat capacity. For example, a sandwich with a thicker or denser bread may retain heat for longer, resulting in a higher overall temperature. On the other hand, a sandwich with a thinner or lighter bread may cool down faster, resulting in a lower overall temperature.

5. How can you ensure the accuracy of the temperature of a hot sandwich?

To ensure the accuracy of the temperature of a hot sandwich, it is important to use precise measurements for the mass and specific heat capacity of the sandwich. Additionally, it is recommended to take multiple readings at different points on the sandwich to account for any variations in temperature. Using a digital thermometer or a thermal camera can also provide more accurate results.

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