A student investigates the cooling of a liquid in a beaker. The temperature $$\(\theta_{\mathrm{R}}\)$$ of the laboratory is measured using a thermometer. The thermometer measures the temperature of the water. At time $$\(t\)$$ the temperature of the water is $$\(\theta\)$$. A series of readings of $$\(t\)$$ and $$\(\theta\)$$ are taken. It is suggested that $$\(\theta\)$$ and $$\(t\)$$ are related by the equation $$\[ \theta=\theta_{\mathrm{R}}+\left(\theta_{0}-\theta_{\mathrm{R}}\right) \mathrm{e}^{-\left(\frac{t}{K}\right)} \]$$ where $$\(\theta_{0}\)$$ is the temperature at $$\(t=0\)$$ and $$\(K\)$$ is a constant. （b）Values of $$\(t\)$$ and $$\(\theta\)$$ are given in Table 2．1． Calculate and record values of $$\(\left(\theta-\theta_{\mathrm{R}}\right) /{ }^{\circ} \mathrm{C}\)$$ and $$\(\ln \left(\left(\theta-\theta_{\mathrm{R}}\right) /{ }^{\circ} \mathrm{C}\right)\)$$ in Table 2．1． Include the absolute uncertainties in $$\(\left(\theta-\theta_{\mathrm{R}}\right)\)$$ and $$\(\ln \left(\left(\theta-\theta_{\mathrm{R}}\right) /{ }^{\circ} \mathrm{C}\right)\)$$ ． ［2］

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