Question

The temperature at $12$ noon was $10°C$ above zero. If it decreases at the rate of $2°C$ per hour until midnight, at what time would the temperature be $8°C$ below zero? What would be the temperature at mid-night?

Answer 1

Step 1: Temperature

1. Temperature is a measure of the average kinetic energy of the atoms or molecules in a system or a physical quantity that represents hot and cold.
2. Heat should not be confused with temperature.

Step 2: Determine the time that would be the temperature be $8°C$ below zero

The temperature at $12$ noon $=10°C$ above zero

The temperature is decreasing at $2°C$ per hour

$8°C$ below zero $=–8°C$

So, total fall in temperature from $10°C$ to $0°C$ and from $0°C$ to $–8°C=18°C$

Since, the temperature falls $2°C$ in every one hour.

Therefore, to decrease $18°C$, time taken $=\frac{18}{2}=9$ hours

The present time is $12$ noon so, the time when the temperature is $–8°C=12$ noon $+9$ hours

So, The time at which the temperature will be $–8°C=9$ PM.

Thus, at $9$ pm temperature would be $8°C$ below zero.

Step 3: Determine the temperature at mid-night

The temperature at $12$ noon $=10°C$

The temperature decreases by $2°C$ every hour.

The temperature decrease in $12$ hours $=–2°C\times 12$

$=–24°C$

At midnight, the temperature will be$=10°C+(-24°C)$

$=-14°C$

Therefore, the temperature at mid night will be $14°C$ below $0$.

So, at $12$ midnight the temperature will be $–14°C$.

Hence, the temperature at midnight is said to be $–14°C$.