Temperature Conversion Explained
The question asks us to find the increase in temperature in degrees Celsius (\(^\circ\)C) when the temperature of a body rises from an initial temperature (\(T_1\)) of \(310\) K to a final temperature (\(T_2\)) of \(340\) K.
Understanding Temperature Scales
Temperature can be measured in different scales, such as Kelvin (K) and Celsius (\(^\circ\)C). The Kelvin scale is an absolute temperature scale, while the Celsius scale is relative to the freezing point of water.
- The relationship between Kelvin and Celsius is given by: \(T(^\circ\text{C}) = T(\text{K}) - 273.15\)
- However, when calculating the temperature difference (increase or decrease), the conversion factor cancels out. This is because a change of 1 Kelvin is equal in magnitude to a change of 1 degree Celsius. \( \Delta T(\text{K}) = T_2(\text{K}) - T_1(\text{K}) \) \( \Delta T(^\circ\text{C}) = T_2(^\circ\text{C}) - T_1(^\circ\text{C}) \) Substituting the conversion formula: \( \Delta T(^\circ\text{C}) = (T_2(\text{K}) - 273.15) - (T_1(\text{K}) - 273.15) \) \( \Delta T(^\circ\text{C}) = T_2(\text{K}) - 273.15 - T_1(\text{K}) + 273.15 \) \( \Delta T(^\circ\text{C}) = T_2(\text{K}) - T_1(\text{K}) \) \( \Delta T(^\circ\text{C}) = \Delta T(\text{K}) \)
Calculating the Temperature Increase
We need to find the change in temperature, \(\Delta T\). We can calculate this difference directly in Kelvin first.
-
Given:
- Initial Temperature, \(T_1 = 310\) K
- Final Temperature, \(T_2 = 340\) K
- Step 1: Calculate the temperature difference in Kelvin. \( \Delta T(\text{K}) = T_2 - T_1 \) \( \Delta T(\text{K}) = 340 \text{ K} - 310 \text{ K} \) \( \Delta T(\text{K}) = 30 \text{ K} \)
- Step 2: Convert the temperature difference to Celsius. As established earlier, the temperature difference in Kelvin is numerically equal to the temperature difference in Celsius. \( \Delta T(^\circ\text{C}) = \Delta T(\text{K}) \) \( \Delta T(^\circ\text{C}) = 30 \text{ K} \) Therefore, the temperature increase is \(30^\circ\)C.
Final Answer
The temperature increase from \(310\) K to \(340\) K is \(30^\circ\)C.
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