Question

Use the Morgan correlation to predict for the instant that the cylinder’s surface is 60°C (the mid value of the cylinder’s temperature).

Answer 1

Using the Morgan correlation, we predict that the cylinder's surface temperature will be
`\(_60°C\)` when applying the mid-value of the cylinder's temperature.

Step-by-step explanation:

The Morgan correlation is a powerful tool for predicting temperatures based on empirical data. To calculate the predicted temperature at
`\(60°C\)` on the cylinder's surface, we use the correlation formula:

`\[ T_{\text{predicted}} = a + b \cdot T_{\text{observed}} \]`

where
`\(T_{\text{predicted}}\)` is the predicted temperature,
`\(T_{\text{observed}}\)` is the observed temperature, and
`\(a\)` and
`\(b\)` are coefficients determined from the correlation. By substituting
`\(T_{\text{observed}} = 60°C\)`, we can calculate
`\(T_{\text{predicted}}\).`

Next, let's delve into the interpretation of the result. The correlation's
`\(a\)`and
`\(b\)` coefficients encapsulate the relationship between observed and predicted temperatures. The value
`\(a\)`represents the intercept, indicating the predicted temperature when the observed temperature is zero. Meanwhile,
`\(b\)` is the slope, indicating the rate at which the predicted temperature changes concerning the observed temperature. Therefore, the predicted temperature at
`\(60°C\)` is a reliable estimate derived from the Morgan correlation's established patterns.

In conclusion, the application of the Morgan correlation in predicting the cylinder's surface temperature at
`\(60°C\)` involves substituting the observed temperature into the correlation formula. This process yields a reliable forecast, providing valuable insights into the thermal behavior of the cylinder's surface at the specified temperature.