UNIT 8 PRACTICE TESTSOLUTIONS

1.

The commercial production of energy by nuclear fusion is not yet possible mainly due to difficulties with

A. obtaining plentiful supplies of a suitable fuel.

B. reaching the high temperatures required.

C. confining the hot plasma.

D. disposing of the radioactive waste products.

2.

It is hypothesized that global warming may lead to significant changes in the average sea-level. This hypothesis

assumes that

A. average rainfall will increase.

B. icebergs will melt.

C. glaciers will melt.

D. the rate of evaporation of seawater will increase.

3.

A wind generator produces 5.0 kW of power for a wind speed of 6.0 m s–1. The best estimate for the power

produced for a wind speed of 12.0 m s–1 is

A. 10 kW. B. 25 kW. C. 40 kW. D. 125 kW.

𝑃 =1

2𝐴𝜌𝑣3

𝑃𝑜𝑤𝑒𝑟 𝑖𝑠 𝑑𝑖𝑟𝑒𝑐𝑡𝑙𝑦 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑎𝑙 𝑡𝑜 𝑡ℎ𝑒 𝑐𝑢𝑏𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

𝐷𝑜𝑢𝑏𝑙𝑖𝑛𝑔 𝑡ℎ𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑤𝑜𝑢𝑙𝑑 𝑟𝑒𝑠𝑢𝑙𝑡 𝑖𝑛 8𝑥 𝑡ℎ𝑒 𝑝𝑜𝑤𝑒𝑟.

8 × 5𝑘𝑊 = 40𝑘𝑊

4.

Two black bodies X and Y are at different temperatures. The temperature of body Y is higher than that of

body X. Which of the following shows the black body spectra for the two bodies?

Inte

nsity

Wavelength (nm)1000 2000 3000 4000 5000

UV

ra

dia

tio

n

IR r

ad

iati

on

vis

ible

ra

dia

tio

n

5.

The diagram below shows a simplified model of the energy balance for Earth. The albedo of the Earth

according to this model is equal to

A. B.

C. D.

.340

2.

340

100

.340

238.

340

240

6.

Nuclear power production

(a) With reference to the concept of fuel enrichment in a nuclear reactor explain,

(i) the advantage of enriching the uranium used in a nuclear reactor.

Fuel enrichment means that the amount of uranium 235 present in the field is increased.

This means more fuel available for fission, therefore the reaction can be sustained.

6.

Nuclear power production

(a) With reference to the concept of fuel enrichment in a nuclear reactor explain,

(ii) from an international point of view, a possible risk to which fuel enrichment could lead.

Enriched fuel can be used in the manufacture of nuclear weapons.

6.

(b) A particular nuclear reactor uses uranium-235 as its fuel source. When a nucleus of uranium-235 absorbs

a neutron, the following reaction can take place.

1. Show that the energy released in the

reaction is approximately 180 MeV.

𝟐. 𝟏𝟖𝟗𝟓 × 𝟏𝟎𝟓 + 𝟗𝟑𝟗. 𝟓𝟔 − 𝟏. 𝟑𝟒𝟎𝟖 × 𝟏𝟎𝟓 + 𝟖. 𝟑𝟕𝟒 × 𝟏𝟎𝟒 + 𝟐 𝟗𝟑𝟗. 𝟓𝟔 = 𝟏𝟖𝟏. 𝟒𝟒 𝑴𝒆𝑽

n2SrXenU 1

0

90

38

144

54

1

0

235

92

6.

(b) A particular nuclear reactor uses uranium-235 as its fuel source. When a nucleus of uranium-235 absorbs

a neutron, the following reaction can take place.

II. State the form in which the energy appears. Kinetic

n2SrXenU 1

0

90

38

144

54

1

0

235

92

6.

(c) The energy released by one atom of carbon-12 during combustion is approximately 4 eV.

I. Using the answer to (b)(i), estimate the ratio

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑜𝑓 𝑐𝑎𝑟𝑏𝑜𝑛 𝑖𝑠 12 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑒𝑛𝑒𝑟𝑔𝑦 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑 𝑖𝑠 4𝑒𝑉.

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑜𝑓 𝑈𝑟𝑎𝑛𝑖𝑢𝑚 𝑖𝑠 235 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑒𝑛𝑒𝑟𝑔𝑦 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑 𝑖𝑠 180 𝑀𝑒𝑉

𝑡ℎ𝑒 𝑟𝑎𝑡𝑖𝑜 𝑖𝑠235 × 180 × 106

12 ×4= 881250000 = 8.8 × 108

6.

(ii) Suggest, with reference to your answer in (c)(i), one advantage of uranium-235 compared with fossil fuels.

The energy density of uranium is much much higher than that of fossil fuel for the same

amount of material.

6.

(d) A sample of waste produced by the reactor contains 1.0 kg of strontium 90 (Sr-90). Sr-90 has a half-life of

9.1 x 108 s.

For the strontium in the sample,

(i) show that its initial activity is 5.1 x 1015 Bq.

Activity = decay constant x number of molecules

l=ln 2

𝑇1/2=

0.69

9×108= 7.6 × 10−10𝑠−1

number of molecules in 1 kg of Sr-90, 1𝑚𝑜𝑙𝑒

90𝑔× 1000𝑔 ×

6.02×1023𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠

1 𝑚𝑜𝑙𝑒= 6.7 × 1024

Activity = (7.6 × 10−10)(6.7 × 1024) = 5.1 × 1015 𝐵𝑞

(ii) calculate its activity after a period of 70 years. (1 yr =3.2 x 107 s)

l= 7.6 × 10−10𝑠−1 3.2 × 107 = 0.02432 𝑦𝑟−1

A = 𝐴0𝑒l𝑡 = 5.1 × 1015 𝑒 −0.02432 70 = 9.29 × 1014𝐵𝑞

(e) Based on your answers to (d), comment on a problem associated with using uranium-235 as an

energy source.

Initial activity is very high; it is still highly radioactive after 70 years, thereby posing a severe

health risk/causing problems for disposal.

7.

This question is about solar power.

(a) Describe, in terms of energy transformations, the difference between a photovoltaic cell and an

active solar heater.

Energy from the sun in the form of light is converted into electrical energy in photovoltaic

cells whereas in the active solar heater, the sun light is converted into thermal energy.

7.

(b) A photovoltaic cell of area 6.5 x 10–4 m2 is situated on the roof of a house. The cell has an efficiency

of 8%. At a time when the power of the solar radiation incident on the photovoltaic cell is a

maximum, the cell delivers a power of 47 mW to the external circuit.

(i) Deduce that the maximum value of the power of the solar radiation incident on the cell is

approximately 0.90 kW m–2 .

𝑷𝒐𝒖𝒕 = 𝟎. 𝟎𝟖𝑷𝒊𝒏 𝑷𝒊𝒏 =𝑷𝒐𝒖𝒕

𝟎.𝟎𝟖=

𝟒𝟕×𝟏𝟎−𝟑

𝟎.𝟎𝟖= 𝟎. 𝟓𝟖𝟕𝟓𝑾

𝑷𝒊𝒏 = 𝑰𝑨 𝑰 =𝑷𝒊𝒏

𝑨=

𝟎.𝟓𝟖𝟕𝟓

𝟔.𝟓×𝟏𝟎−𝟒= 𝟗𝟎𝟑. 𝟖𝑾𝒎−𝟐 = 𝟎. 𝟗𝟎 𝒌𝑾𝒎−𝟐

7.

b(ii) State one reason why the power of solar radiation at any particular region does not have a constant

value.

The amount of sunlight varies from seasons and time of the day.

7.

(c) A power of 3.0 kW is required to produce adequate hot water for the house.

(i) Use the data from (b) to determine the minimum area of the photovoltaic cells required to generate this

power.

𝑷𝒐𝒖𝒕 = 𝟎. 𝟎𝟖𝑰𝑨 𝑨 =𝑷𝒐𝒖𝒕

𝟎. 𝟎𝟖𝑰=

𝟑 × 𝟏𝟎𝟑

(𝟎. 𝟎𝟖)(𝟗𝟎𝟑. 𝟖)= 𝟒𝟏. 𝟓 𝒎𝟐

𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒄𝒆𝒍𝒍𝒔 =𝒕𝒐𝒕𝒂𝒍 𝒂𝒓𝒆𝒂

𝒕𝒐𝒕𝒂𝒍 𝒂𝒓𝒆𝒂 𝒑𝒆𝒓 𝒄𝒆𝒍𝒍=

𝟒𝟏.𝟓

𝟔.𝟓×𝟏𝟎−𝟒= 𝟔𝟑𝟖𝟒𝟔. 𝟏𝟓 𝒄𝒆𝒍𝒍𝒔 = 𝟔𝟑𝟖𝟒𝟕 𝒄𝒆𝒍𝒍𝒔

7.

The efficiency of energy conversion in an active solar heater is 24%. Calculate the minimum area of this solar

heater required to generate this power.

𝑷𝒐𝒖𝒕 = 𝟎. 𝟐𝟒𝑰𝑨 𝑨 =𝑷𝒐𝒖𝒕

𝟎.𝟎𝟖𝑰=

𝟑×𝟏𝟎𝟑

(𝟎.𝟐𝟒)(𝟗𝟎𝟑.𝟖)= 𝟏𝟑. 𝟖𝒎𝟐

7.

(iii) State and explain whether it is more practical to use photovoltaic cells or an active solar heater to

provide hot water for the house.

The active solar heater requires less area, it’s cheaper, and storage is easy.

8.

This question is about power generation.

(a) Describe the origin of fossil fuels.

Organic or living matter dies and decomposed. The decomposition is compressed by high

temperature and pressure.

8.

(b) An electrical power generating station using fossil fuels as its source of energy has an output of 2 GW. It

has been suggested that this station should be replaced by wind turbines, each providing 0.8 MW of electrical

power.

(i) State two advantages of the use of wind power.

The energy source is renewable and no carbon emission.

8.

(ii) State and explain two disadvantages of using wind turbines to replace the fossil-fuel generating station.

To get most out of the wind turbines, you will need a lot of them and a lot of space.

The output is inconsistent and unreliable, and dependent on wind speed.

Change in local climate as a result of turbulence.

9.

This question is about a wind turbine.

Air of density r and speed v passes normally through an area A.

(a) Deduce that the kinetic energy of the air passing through the area per unit time is given by the

expression

𝒎𝒂𝒔𝒔 𝒊𝒏𝒄𝒊𝒅𝒆𝒏𝒕 𝒑𝒆𝒓 𝒖𝒏𝒊𝒕 𝒕𝒊𝒎𝒆 = 𝑨𝝆𝒗

𝒌𝒊𝒏𝒆𝒕𝒊𝒄 𝒆𝒏𝒆𝒓𝒈𝒚 =𝟏

𝟐𝒎𝒗𝟐 =

𝟏

𝟐𝑨𝝆𝒗 𝒗𝟐 =

𝟏

𝟐𝝆𝑨𝒗𝟑

kinetic energy per unit time = 1

2𝜌𝐴𝑣3

9.Air of constant density 1.2 kg m–3 is incident at a speed of 9.0 m s–1 on the blades of a wind turbine. The

turbine blades are each of length 7.5 m. The air passes through the turbine without any change of direction.

Immediately after passing through the blades, the speed of the air is 5.0 m s–1 as illustrated below.

𝑷 =𝟏

𝟐𝝆𝑨𝒗𝟑 =

𝟏

𝟐(𝟏. 𝟐)𝝅(𝟕. 𝟓)𝟐(𝟗)𝟑 −

𝟏

𝟐(𝟐. 𝟐)𝝅(𝟕. 𝟓)𝟐(𝟓)𝟑 = 𝟓𝟑𝒌𝑾

wind speed wind speed

9.0 m s–1

5.0 m s–1

turbine blades

The density of air immediately after passing through the blades is 2.2

kg m–3. The turbine and generator have an overall efficiency of 72%.

(b) Calculate

(i) the power extracted from the air by the turbine;

9.

(ii) the electrical power generated.

𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 × 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛𝑝𝑢𝑡

𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 = 0.72 × 53𝑘𝑊 = 38 𝑘𝑊