The relation of heat (Q), mass (m), and change of temperature (ΔT) is given by the formula:
Q = m*Cs*ΔT, where Cs is the specific heat of the material.
Then, given than you know Q, m and ΔT, you can solv for Cs:
Cs = Q / (m*ΔT)
Cs = 89.6 J / [20 grams * (40.0°C - 30.0°C)] = 0.448 J / g * °C.
Explanation:
a) Using the provided information about the density of gold, the sample size, thickness, and the following equations and comersion factors, find the area of the gold leaf:

Gold 

First, find the volume of the sample and then find the area of the sample.


b. Using the provided information from part
), the radius of the cylinder, and the following equation for the volume of a cylinder, find the length of the fiber :


Is this multiple choice? Is there any educational problem that really needs to be solved?
If you ask me I think a helicopter would be fastest, just sayin.
Boyle's law of ideal gas: This law states that the volume of a gas is inversely proportional to its pressure at a constant temperature. Acc to this law we can write the relation of pressure and volume as:

That means:

From that equation we can calculate Volume of gas at a certain pressure:
P₁=Initial pressure
V₁=Initial volume
P₂=Final pressure
V₂= Final volume
Here P₁, initial pressure is given as 85.0 kPa
V₁, initial volume is given as 525 mL
P₂, final pressure is 65.0 kPa

so,
V_{2}=85\times 525\div 65
=686 mL
Volume of gas will be 686 mL.
Hydrogenated vegetable oil is a preservative, thus, the correct option is D. Hydrogenated vegetable oil are used by food industries to prevent fat rancidity in order to give their product a longer shelf life. Hydrogenated oils are very good preservatives because all the enzymatic activities in the oil has been neutralized during the hydrogenating process.