Um cientista dispõe de um termômetro de mercúrio com a escala totalmente ilegível. Desejando medir a temperatura de uma substância X com o termômetro, ele adotou o seguinte procedimento: sob a condição de pressão normal (1 atm), mergulhou o termômetro na água em ebulição e observou que a coluna de mercúrio atingiu o comprimento de 10 cm; posteriormente, colocando o termômetro em gelo fundente, o comprimento da coluna de mercúrio passou a ser de 2 cm. Após esse procedimento, ele colocou o termômetro em contato com a substância X e encontrou o comprimento de 5,2 cm para a coluna de mercúrio. Baseado nessas informações, a temperatura da substância X medida pelo cientista, em graus Celsius, é de
- A) 65 °C
- B) 52 °C
- C) 48 °C
- D) 40 °C
- E) 32 °C
Resposta:
To determine the temperature of substance X, the scientist used a thermometer with an illegible scale. However, by calibrating the thermometer using the boiling point of water (100°C) and the freezing point of water (0°C), we can determine the temperature of substance X.
When the thermometer was placed in boiling water, the mercury column reached a length of 10 cm. When it was placed in melting ice, the mercury column reached a length of 2 cm. Using these two points, we can create a rough scale for the thermometer.
Let's assume the scale is linear, and the distance between the two points is 8 cm (10 cm - 2 cm). The boiling point of water is 100°C, and the freezing point of water is 0°C. We can set up a proportion to relate the distance on the thermometer to the temperature:
$$frac{8 cm}{100°C - 0°C} = frac{x cm}{T°C - 0°C}$$When the thermometer was placed in contact with substance X, the mercury column reached a length of 5.2 cm. We can use the proportion to find the temperature of substance X:
$$frac{8 cm}{100°C - 0°C} = frac{5.2 cm}{T°C - 0°C}$$Solving for T, we get:
$$T = frac{5.2 cm}{8 cm} times 100°C = 40°C$$Therefore, the correct answer is option D) 40°C.
This problem demonstrates the concept of calibration and the use of proportional relationships to solve problems in physics. By using the known boiling and freezing points of water, we can create a rough scale for the thermometer and determine the temperature of substance X.
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