Question

A certain freezing process requires that room temperature be lowered from ${40^ \circ }C$ at the rate of ${5^ \circ }C$ every hour. What will be the room temperature 10 hours after the process begins?

Answer 1

Hint: In this question use the given information to identify the given values and also remember that \[\dfrac{{dT}}{{dt}} = -{5^ \circ }C\] which means every hour temperature will decrease by ${5^ \circ }C$, use this information to approach the solution.

Complete step-by-step solution:
According to the given information we know a room where the present temperature is ${40^ \circ }C$
So, for freezing process we have to lower the room temperature and the rate at which the room temperature is lowered every hour is ${5^ \circ }C$ i.e. \[\dfrac{{dT}}{{dt}} = -{5^ \circ }C\]
To find what will be the room temperature 10 hours after the process begins
Present temperature = ${40^ \circ }C$
Since the change in rate of temperature is \[\dfrac{{dT}}{{dt}} = -{5^ \circ }C\] which means in each hour temperature will drop by ${5^ \circ }C$
Therefore, after 10 hours the temperature will be drop by $-{5^ \circ }C \times 10$
Change in temperature after 10 hours = ${50^ \circ }C$
Therefore, temperature after 10 hours= ${40^ \circ }C - {50^ \circ }C$
So, the room temperature 10 hours after the process starts = $ - {10^ \circ }C$.

Note: The trick behind these types of questions is first to identify the initial temperature and the rate of change in temperature then as we knew that we require the change in temperature after 10 hours so it is a basic concept that if in an hour the change in temperature is ${5^ \circ }C$ so after 10 hours the change in temperature will be the multiplication of rate of change in temperature per hour and the time after finding the change in temperature after 10 hours we can subtract the initial temperature with the change in temperature to find the final temperature required.