The temperature 𝑇 , in celsius, of an object removed from a freezer is determined by the formula
d𝑇/d𝑡=−𝑘(𝑇−𝑇0)
for a constant 𝑘 and 𝑇0 is the room temperature and 𝑡 is in hours.
What are the units of 𝑘?
The units of 𝑘 can be determined using the units of each term in the equation:
d𝑇/d𝑡: temperature change per time, in degrees Celsius per hour
𝑘: a constant, units are determined by rearranging the equation to solve for 𝑘:
𝑘 = -(d𝑇/d𝑡) / (𝑇−𝑇0)
Therefore, the units of 𝑘 are (degrees Celsius per hour) / (degrees Celsius), which simplifies to 1/hour.