Chapter 3, Problem 3.1P

What is $\text{1 cal}$ in SI units and what is the name given to $\text{1 N}-\text{m}$ ?

To determine

The value of 1 calorie in SI units.

The conversion of 1N-m.

Answer to Problem 3.1P

The value of 1 calorie in SI units is $1Cal=\mathrm{4.186.1}J$.

The conversion of 1N-m is 1 joule.

Explanation of Solution

Given:

A quantity of $1\text{cal}$.

A quantity of $1\text{Nm}$.

Calculation:

A calorie is anamount of heat energy that is required to increase the temperature of one gram of water $1^{\circ }C$ .According to the requirement of the amount of heat, a calorie is also referred to as a small calorie (Cal) and a larger calorie (kcal).

A calorie is the unit of energy content In the SI system, 1 calorie equals to the $4.186Joule$.

As it is already explained above that, $1cal=\mathrm{4.186.1}J$.

Therefore,

  $\begin{array}{c}1Cal=\mathrm{4.186.1}J\\ =4.186N·m\\ =4.186\frac{kg·m^2}{s^2}\end{array}$

The explanation for the conversion of $1N·m$ - It equals 1 joule. It is also used as a unit of energy.

Joule is also a standard unit of energy or work in the SI (International System of units) system. It is denoted by the symbol J.

In the SI system of measurement,

  $\begin{array}{l}1cal=\mathrm{4.186.1}J=1N·m=1\frac{kg·m^2}{s^2}\\ \end{array}$.

Therefore, $1N·m$ can be converted to 1 joule.