A student investigates the cooling of a liquid in a beaker. The temperature $$\(\theta_{\mathrm{R}}\)$$ of the laboratory is measured using a thermometer. The thermometer measures the temperature of the water. At time $$\(t\)$$ the temperature of the water is $$\(\theta\)$$. A series of readings of $$\(t\)$$ and $$\(\theta\)$$ are taken. It is suggested that $$\(\theta\)$$ and $$\(t\)$$ are related by the equation $$\[ \theta=\theta_{\mathrm{R}}+\left(\theta_{0}-\theta_{\mathrm{R}}\right) \mathrm{e}^{-\left(\frac{t}{K}\right)} \]$$ where $$\(\theta_{0}\)$$ is the temperature at $$\(t=0\)$$ and $$\(K\)$$ is a constant. （c）（i）Plot a graph of $$\(\ln \left(\left(\theta-\theta_{\mathrm{R}}\right) /{ }^{\circ} \mathrm{C}\right)\)$$ against $$\(t / \min\)$$ ．Include error bars for $$\(\ln \left(\left(\theta-\theta_{\mathrm{R}}\right) /{ }^{\circ} \mathrm{C}\right)\)$$ ． ［2］ （ii）Draw the straight line of best fit and a worst acceptable straight line on your graph．Label both lines． ［2］ （iii）Determine the gradient of the line of best fit．Include the absolute uncertainty in your answer． gradient＝ ..................................................... ［2］ (iv) Determine the $$\(y\)$$-intercept of the line of best fit. Include the absolute uncertainty in your answer. y-intercept = .....................................................

Answer:

Knowledge points:

Solution: