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What is the pressure of a cavity that has 17 cm on its longest axis, the other two measures 15 and 23 cm. A volume of 4600cm3

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Answer to a math question What is the pressure of a cavity that has 17 cm on its longest axis, the other two measures 15 and 23 cm. A volume of 4600cm3

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Rasheed
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107 Answers
Para encontrar a pressão de uma cavidade, podemos usar a fórmula da pressão em um gás, que é dada por:

P = \frac{nRT}{V}

onde:
- P é a pressão do gás (que queremos encontrar)
- n é o número de mols do gás (vamos assumir que seja 1 mol)
- R é a constante dos gases (0.082 atm L / mol K)
- T é a temperatura do gás (não foi fornecida no problema)
- V é o volume do gás (4600 cm³)

Além disso, usaremos a fórmula do volume de uma elipse, que é dada por:

V_{elipse} = \frac{4}{3}\pi abc

onde:
- a, b e c são os semi-eixos da elipse

Neste caso, como a cavidade é elipsoidal e possui os eixos de medidas 17 cm, 15 cm e 23 cm, temos que a = 17/2, b = 15/2 e c = 23/2.

Substituindo na fórmula do volume da elipse:

4600 = \frac{4}{3}\pi \times \frac{17}{2} \times \frac{15}{2} \times \frac{23}{2}

4600 = \frac{4}{3}\pi \times \frac{17 \times 15 \times 23}{8}

4600 = \frac{4}{3}\pi \times \frac{5865}{8}

4600 = \frac{4}{3}\pi \times 733.125

4600 = 977.5\pi

\pi = \frac{4600}{977.5} \approx 4.71 \, \text{cm}^2

Agora podemos substituir o valor de \pi encontrado e o volume na fórmula da pressão:

P = \frac{1 \times 0.082 \times T}{4600}

P = \frac{0.082T}{4600}

Portanto, a pressão da cavidade é \frac{0.082T}{4600} atm.

\boxed{P = \frac{0.082T}{4600} \, \text{atm}}

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