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.

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.

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.

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.

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.

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.

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.

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.