A certain freezing process requires that room temperature be lowered from `40^@` C at the rate of `5^@`C per hour. What will be the room temperature `12` hours after the process begins?

Options

A. `-21^@C`
B. `-20^@C`
C. `-16^@C`
D. `-18^@C`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the initial temperature
The initial room temperature is given as:
\[ \text{Initial Temperature} = 40^\circ C \]

### Step 2: Determine the rate of temperature decrease
The rate at which the temperature decreases is:
\[ \text{Rate of decrease} = 5^\circ C \text{ per hour} \]

### Step 3: Calculate the total decrease in temperature over 12 hours
To find out how much the temperature will decrease in 12 hours, we multiply the rate of decrease by the number of hours:
\[ \text{Total decrease} = \text{Rate of decrease} \times \text{Time} = 5^\circ C \times 12 \text{ hours} = 60^\circ C \]

### Step 4: Calculate the final temperature
Now, we subtract the total decrease from the initial temperature to find the final temperature:
\[ \text{Final Temperature} = \text{Initial Temperature} - \text{Total decrease} = 40^\circ C - 60^\circ C \]
\[ \text{Final Temperature} = -20^\circ C \]

### Conclusion
The room temperature after 12 hours will be:
\[ \text{Final Temperature} = -20^\circ C \]

---