*Question*

Which of the energy sources are classified as renewable and non-renewable?

**▶️Answer/Explanation**

## Markscheme

C

*Question*

Which change produces the largest percentage increase in the maximum theoretical power output of a wind turbine?

A Doubling the area of the blades

B Doubling the density of the fluid

C Doubling the radius of the blades

D Doubling the speed of the fluid

**▶️Answer/Explanation**

Ans: D

Power Delivered by Wind Generator:

Assume a rotor blade radius of *r*. ∙

The volume of air that moves through the blades in a time *t* is given by

*V* = *Ad* = *Avt*, where *v* is the speed of the air and *A* = π*r*^{2}.

The mass *m* is thus *m* = ρ*V* = ρ*Avt*.

*E*_{K} = (1/2)*mv*^{2} = (1/2)ρ*Avtv*^{2} = (1/2)ρ*Av*^{3}*t*.

Power is \(\frac{E_K}{t}\) so that

\(\frac{E_K}{t}=\frac{1}{2} A\rho v^3\)

Where \(A = \pi r^2\)

*Question*

A wind turbine has a power output *p *when the wind speed is *v*. The efficiency of the wind turbine does not change. What is the wind speed at which the power output is \(\frac{p}{2}\)?

A. \(\frac{v}{4}\)

B. \(\frac{v}{{\sqrt 8 }}\)

C. \(\frac{v}{2}\)

D. \(\frac{v}{{\sqrt[3]{2}}}\)

**▶️Answer/Explanation**

## Markscheme

D

power output is given by equation.

\(\frac{E_K}{t}=\frac{1}{2} A\rho v^3\)

Where \(A = \pi r^2\)

\(p=\frac{1}{2} A\rho v^3\) — equation (1)

Given that at power \(p\) velocity \(v\)

Now for power \(\frac{p}{2}=p’\)

Hence

\(p’ = \frac{1}{2} A\rho v’^3\)

or

\(\frac{p}{2}=\frac{1}{2} A\rho v’^3\) –eq (2)

or

From equation (1) and (2) we get

\(\frac{\frac{1}{2} A\rho v’^3}{\frac{1}{2} A\rho v^3}=\frac{1}{2}\)

or

\(v’^3 =\frac{1}{2} v^3\)

or

\(v’=\frac{v}{\sqrt[3]{2}}\)

*Question*

Three energy sources for power stations are

I. fossil fuel

II. pumped water storage

III. nuclear fuel.

Which energy sources are primary sources?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

**▶️Answer/Explanation**

### Markscheme

B

Primary and Secondary Sources

Primary Energy Sources | Secondary Energy Sources |

Energy sources found in the natural environment (fossil fuels, solar, wind, nuclear, hydro, etc.) | Useful transformations of the primary sources (electricity, pumped storage for hydro, etc.) |

*Question*

What is equivalent to \(\frac{{{\text{specific energy of a fuel}}}}{{{\text{energy density of a fuel}}}}\)?

A. density of the fuel

B. \(\frac{1}{{{\text{density of the fuel}}}}\)

C. \(\frac{{{\text{energy stored in the fuel}}}}{{{\text{density of the fuel}}}}\)

D. \(\frac{{{\text{density of the fuel}}}}{{{\text{energy stored in the fuel}}}}\)

**▶️Answer/Explanation**

## Markscheme

B

* Specific energy*, E

_{S}is the amount of energy that can be extracted from a unit mass of fuel.

* Energy density, *E

_{D}is the amount of energy that can be extracted from a unit volume of fuel mass.

They are related by

\(E_D=\frac{mass}{volume}E_s\)

or

\(\frac{E_s}{E_D}=\frac{Volume}{mass}=\frac{1}{\text {density of fuel}}\)

*Question*

The energy density of a substance can be calculated by multiplying its specific energy with which quantity?

A. mass

B. volume

C. \(\frac{{{\text{mass}}}}{{{\text{volume}}}}\)

D. \(\frac{{{\text{volume}}}}{{{\text{mass}}}}\)

**▶️Answer/Explanation**

## Markscheme

C

* Specific energy*, E

_{S}is the amount of energy that can be extracted from a unit mass of fuel.

* Energy density, *E

_{D}is the amount of energy that can be extracted from a unit volume of fuel mass.

They are related by

\(E_D=\frac{mass}{volume}E_s\)

or

\(\frac{E_s}{E_D}=\frac{Volume}{mass}=\frac{1}{\text {density of fuel}}\)

*Question*

Which of the energy sources are classified as renewable and non-renewable?

**▶️Answer/Explanation**

## Markscheme

C