# Problem № 8 (15 points)

In some English-speaking countries, temperature is measured in degrees Fahrenheit. An English schoolboy, observing a thermometer in a glass of cooling water, noticed that it cooled by $10^{\circ} \mathrm{F}$. He became curious about how much heat was released. In books, he found the following formula that allows calculating the answer to his question: $Q=4200 \cdot V \cdot \Delta T$, where $V$ is the volume of water in liters, $\Delta T$ is the change in its temperature. However, the change in temperature in this formula must be substituted in degrees Celsius. Degrees Fahrenheit are related to degrees Celsius by the following relationship ${ }^{\circ} F={ }^{\circ} C \cdot \frac{9}{5}+32$. What result should he get if he had 1 liter of water at his disposal?
# Answer: 23.3 kJ

## Solution and grading criteria:

The change in temperature in degrees Fahrenheit is related to the change in temperature in degrees Celsius:

![](https://cdn.mathpix.com/cropped/2024_05_06_2e80d2c4d366657d3790g-3.jpg?height=103&width=1182&top_left_y=1879&top_left_x=197)

That is, in degrees Celsius, the water cooled by: \(\Delta^{\circ} \mathrm{C} = \frac{5}{9} \cdot \Delta^{\circ} F = \frac{5}{9} \cdot 10 \sim 5.56^{\circ} \mathrm{C}\).

Therefore, the amount of heat released is:

\(Q = 4200 \cdot V \cdot \Delta T = 4200 \cdot 1 \cdot 5.56 \approx 23.3 \kappa\) J

(4 points)

![](https://cdn.mathpix.com/cropped/2024_05_06_2e80d2c4d366657d3790g-4.jpg?height=357&width=352&top_left_y=193&top_left_x=161)

## Multidisciplinary Engineering Olympiad "Star" in Natural Sciences

## Final Stage

2016-2017 academic year

## Problems, answers, and grading criteria

![](https://cdn.mathpix.com/cropped/2024_05_06_2e80d2c4d366657d3790g-4.jpg?height=123&width=525&top_left_y=641&top_left_x=937)

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