A separable rate model and interpretation · Short practice
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Recall
A separable cooling model — objective 1
Maths4U Original · Short practice
A sealed sensor is initially at 34°C in surroundings held at 16°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{1}{5}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find the initial excess temperature above ambient.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
A separable cooling model — objective 1
Maths4U Original · Short practice
A sealed sensor is initially at 37°C in surroundings held at 17°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{3}{10}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find the initial excess temperature above ambient.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Method
A separable cooling model — objective 2
Maths4U Original · Short practice
A sealed sensor is initially at 37°C in surroundings held at 17°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{3}{10}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find T at \(\displaystyle t= \frac{\ln 2}{k}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
A separable cooling model — objective 2
Maths4U Original · Short practice
A sealed sensor is initially at 28°C in surroundings held at 18°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{1}{10}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find T at \(\displaystyle t= \frac{\ln 2}{k}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Apply
A separable cooling model — objective 3
Maths4U Original · Short practice
A sealed sensor is initially at 28°C in surroundings held at 18°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{1}{10}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find the limiting temperature as t tends to infinity.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
A separable cooling model — objective 3
Maths4U Original · Short practice
A sealed sensor is initially at 31°C in surroundings held at 19°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{1}{5}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find the limiting temperature as t tends to infinity.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Check understanding
A separable cooling model — objective 4
Maths4U Original · Short practice
A sealed sensor is initially at 31°C in surroundings held at 19°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{1}{5}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find the half-life of the excess, divided by ln2.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fresh review variant
A separable cooling model — objective 4
Maths4U Original · Short practice
A sealed sensor is initially at 29°C in surroundings held at 15°C. Its temperature rate in °C per minute is proportional to its excess above ambient, with positive cooling constant \(\displaystyle k=\)\(\displaystyle \frac{3}{10}\) min⁻¹. Assume this model applies for all \(\displaystyle t\ge 0\).
Find the half-life of the excess, divided by ln2.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.