Question

The temperature of a chemical reaction oscillates in the interval 44 degrees Celsius to 50 degrees Celsius. The temperature is at 47 degrees Celsius at t=0 and rises at the start of a four-minute cycle. Which function represents the relationship between time, t, and temperature, T?

Answer 1

47 +3 sin(
`sin((2\pi )/(4)t )`)

Explanation:

Here temperature of reaction oscillates about 47.

Temperature amplitude is 3.

Most popular and simple function which can describe the temperature is sinosuidal function.

We know sinosuidal function can be negative as well as positive with magnitude as it's amplitude.

We need angular frequency for this.

Time period is given =4 min

Angular frequency =
`(2\pi )/(T)` =
`(2\pi )/(4)`

So temperature as a function of time is

T(t) = 47 + sin(
`47 +sin((2\pi )/(4)t )`)