Chapter 1, Problem 52A

(a)

To determine

Average temperature change per hour.

Answer to Problem 52A

  $-1.17°\text{C}/\text{h}$

Explanation of Solution

Given:

Change in temperature:

  $\begin{array}{c}\Delta T=10°\text{C}-24°\text{C}\\ =-14°\text{C}\end{array}$

Time for temperature change, $t=12\text{h}$

Formula used:

Average change in temperature per hour is given by the following formula:

  $s=\frac{\Delta T}{t}$

Calculation:

Average change in temperature,

  $s=-\frac{14°\text{C}}{12\text{h}}$

  $s=-1.17 \frac{\text{°C}}{\text{h}}$

Minus sign indicates that temperature decreases with time.

Conclusion:

Average rate of temperature change is $-1.17°\text{C}/\text{h}$ .

(b)

To determine

Temperature in 2 hours if trends continue.

Answer to Problem 52A

  $7.66°\text{C}$

Explanation of Solution

Given:

Time, $t=\text{2 h}$

Average rate of temperature change: $-1.17°\text{C}/\text{h}$

Initial temperature, $T_i=10\text{°C}$

Formula used:

Average rate of temperature change is given by:

  $s=\frac{T_f-T_i}{t}$

Where,

  $T_f$ = final temperature

Calculation:

Final temperature is,

  $-1.17=\frac{T_f-10}{2}$

  $T_f-10=-1.17\times 2$

  $T_f-10=-2.34$

  $T_f=10-2.34$

  $T_f=7.66°\text{C}$

Conclusion:

Temperature after 2 hours is $7.66°\text{C}$ .

(c)

To determine

Prediction of temperature in 24 hours.

Answer to Problem 52A

Yes, we can predict temperature accurately in 24 hours.

Temperature in 24 hours is $-4.08°\text{C}$ .

Explanation of Solution

We know the rate of temperature change with time; therefore, we can predict temperature accurately in 24 hour.

Given:

Time, $t=24\text{h}$

Average rate of temperature change: $-1.17°\text{C}/\text{h}$

Initial temperature $T_i=24°\text{C}$

Formula used:

Average rate of temperature change is given by:

  $s=\frac{T_f-T_i}{t}$

Where,

  $T_f$ = final temperature

  $-1.17=\frac{T_f-24}{24}$

  $T_f-24=-1.17\times 24$

  $T_f-24=-28.08$

  $T_f=24-28.08$

  $T_f=-4.08°\text{C}$

Conclusion:

Temperature after 24 hours is $-4.08°\text{C}$ .