IBDP Physics 8.1 – Energy sources : IB style Question Bank SL Paper 1

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 = πr2.

The mass m is thus m = ρV = ρAvt.

EK = (1/2)mv2 = (1/2)ρAvtv2 = (1/2)ρAv3t.

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, ES is the amount of energy that can be extracted from a unit mass of fuel.

Energy density, ED 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, ES is the amount of energy that can be extracted from a unit mass of fuel.

Energy density, ED 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