Young's Modulus is equal to the stress over strain on an object. The stress on an object refers to the pressure that is put on an object, and can be given the below equation.

$\displaystyle Stress=\frac{F}{A}$

The strain on an object refers to the amount an object is deformed in the direction of the force. It can be given the below equation, where $\displaystyle \Delta L$ is the change in length and $\displaystyle L$ is the original length.

$\displaystyle Strain=\frac{\Delta L}{L}$

Combining these two equations we can determine Young's Modulus.

$\displaystyle \frac{stress}{strain}= \frac{\frac{F}{A}}{\frac{\Delta L}{L}}= \frac{FL}{A\Delta L}$

To find the right answer, we need to know two formulas:

$\displaystyle K = C + 273$

$\displaystyle F = (1.8)(^oC) +32$

The simplest way to compare these choices will be to convert them all to Kelvin.

$\displaystyle 100K$

$\displaystyle 400K$

$\displaystyle 42^oC = 42+ 273 = 315K$

$\displaystyle 150^oF = (1.8)(^oC) + 32$

$\displaystyle \rightarrow ^oC=\frac{150-32}{1.8}=65.6^oC$

$\displaystyle \rightarrow 65.6+273=338.6K$

$\displaystyle 140^oC = 140 + 273 = 413K$

This makes our answer $\displaystyle 140^oC$.

$\displaystyle 100K< 42^oC< 150^oF< 400K< 140^oC$

In this question, you will have to use the given equation twice; once for melting point and once for boiling point. Let’s first convert the melting point to Fahrenheit. The question states that the melting point of water is $\displaystyle 0^{\circ}C$. Plugging this into the equation gives:

$\displaystyle ^oF=(\frac{9}{5})^oC+32$

$\displaystyle ^oF=(\frac{9}{5})(0^oC)+32$

$\displaystyle F = 32^{\circ}F$

The melting point of water is $\displaystyle 32^{\circ}F$. Similarly, we convert the boiling point of water to Fahrenheit:
$\displaystyle ^oF=(\frac{9}{5})(100^oC)+32$

$\displaystyle ^oF=180+32$

$\displaystyle F = 212^{\circ}F$

The boiling point is $\displaystyle 212^{\circ}F$. The difference between boiling point and melting point in Fahrenheit is:
$\displaystyle 212^{\circ}F - 32^{\circ}F = 180^{\circ}F$

Kelvin is a temperature scale that is named after Lord Kelvin. Lord Kelvin, through his experiments, found that absolute zero $\displaystyle (0K)$ occurs at a temperature of $\displaystyle -273.15^{\circ}C$. Later, scientists defined Kelvin as the fraction $\displaystyle (\frac{1}{273.16})$ of the temperature of water at its triple point (the point on a phase diagram at which water exists as a solid, a liquid, and a gas). This is because the temperature at the triple point of water, in Celsius, is $\displaystyle 0.01^{\circ}C$. In Kelvin scale, the triple point of water occurs at $\displaystyle 273.16K$.

$\displaystyle 273.15+0.01^oC=273.16K$

The question states that the melting point of iron is $\displaystyle 2800^{\circ}F$. We can use the given equation to convert this to Celsius.

$\displaystyle ^oF=(\frac{9}{5})^oC+32$

$\displaystyle ^oC=(^oF-32)(\frac{5}{9})$

$\displaystyle ^oC=(2800^oF-32)(\frac{5}{9})$

$\displaystyle C=1538^oC$

This means that the melting point of iron is $\displaystyle 1538^{\circ}C$. At this point you can choose the right answer because there is only one answer option that has $\displaystyle 1538^{\circ}C$; however, let’s solve for Kelvin. The second equation you need to know is the conversion from Celsius to Kelvin:

$\displaystyle K=^oC+273.15$

The melting point of iron in Kelvin is:

$\displaystyle K=1538^oC+273.15=1811K$