# 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 $30^{\circ} \mathrm{F}$. 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 2 liters of water at his disposal?
# Answer: 140 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-6.jpg?height=114&width=1200&top_left_y=2070&top_left_x=188)

That is, in degrees Celsius, the water cooled by: $\Delta^{\circ} \mathrm{C}=\frac{5}{9} \cdot \Delta^{\circ} F=\frac{5}{9} \cdot 30 \approx 16.67^{\circ} \mathrm{C}$.

Therefore, the amount of heat released is:

$Q=4200 \cdot V \cdot \Delta T=4200 \cdot 2 \cdot 16.67 \approx 140$ kJ