Chapter 24, Problem 31A

To determine

The temperature of the day when cold is twice.

Answer to Problem 31A

  $-131.575°\text{C or }141.575\text{ K}$

Explanation of Solution

Given:

Temperature of the day, $T=10°\text{C}$

Formula used:

  $T\left(\text{in K}\right)=T\left(\text{in}°\text{C}\right)+273.15$

Calculation:

Change the temperature of day in kelvin,

  $\begin{array}{c}T\left(\text{in K}\right)=T\left(\text{in }°\text{C}\right)+273.15\\ =10°\text{C}+273.15\\ =283.15\text{ K}\end{array}$

Your friend wishes the twice cold and air had half the internal energy. So, temperature will become half.

  $\begin{array}{c}{T}_c=\frac{T}{2}\\ =\frac{283.15}{2}\\ =141.575\text{ K}\end{array}$

Now, by changing in degree Celsius,

  $\begin{array}{c}{T}_c\left(\text{in }°\text{C}\right)=T_c\left(\text{in K}\right)-273.15\\ =141.575-273.15\\ =-131.575°\text{C}\end{array}$

Conclusion:

The temperature of the cold day will be $141.575\text{ K}$ or $-131.575°\text{C}$ .