Assignment 9

Thermodynamics

Introduction

Aims

This assignment will test your ability to: ? answer multiple-choice questions ? describe practical situations and interpret measurements.

You do not need to have studied the physics that underlies these experiments in order to be able to complete the tasks.

Links to the assessment requirements

The assessment objectives for the A level that are relevant to this assignment are to:

n apply knowledge and understanding of scientific ideas,

processes, techniques and procedures: ? in a practical context ? when handling qualitative data ? when handling quantitative data

n analyse, interpret and evaluate scientific information, ideas and evidence, including in relation to issues, to: ? make judgements and reach conclusions ? develop and refine practical design and procedures.

How your tutor will mark your work

Your tutor will assess the following aspects of your work: ? your application of appropriate physical principles ? your use of appropriate equations ? the accuracy of your calculations ? your use of graphs and drawings where directed ? your use of appropriate units.

Are you ready to do this assignment?

Before you tackle this assignment, ensure that you have studied Section 9 of the course and Chapters 10, 11 and 12 of the textbook. In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler and protractor, graph paper and a calculator.

The assignment

In calculations, use g = 9.81 m s–2 for the acceleration of free fall unless told otherwise. Data for other questions can be found in the Data booklet, which is linked to Section 6.

1 Figure 1 shows the variation of temperature with time of a sample of ice, turning into water. In what region(s) do ice and water coexist in equilibrium?

Figure 1 Illustration for Question 1

(a) Between A and B. (b) Between B and C.

(c) Between C and D.

(d) None of these regions. (1 mark)

2 A fixed mass of gas has a volume V. If the temperature is changed such that the root mean square velocity of the molecules of the gas is doubled, while the pressure remains constant, what is the new volume of the gas?

(a) V

(b) 1.4 V

(c) 2 V

(d) 4 V

(1 mark)

3 A volume of gas has a pressure 1.5 × 104 Pa at 0 ºC. If the volume is kept constant, to what temperature must it be heated to reach a pressure of 2.1 × 104 Pa?

(a) 382 K

(b) 164 K

(c) 455 K

(d) 195 K

(1 mark)

4 Which of the following statements correctly describes the energy of water molecules when they are being changed from the solid state to the liquid state at 0 ºC?

(a) The internal energy stays the same.

(b) Their kinetic energy is increasing.

(c) Their internal energy falls.

(d) Their kinetic energy stays the same.

(1 mark)

5 50 g of water at 40 ºC is placed in a well-insulated container. Neglecting heat losses, what mass of ice at 0 ºC must be added to reduce the temperature of the water to 12 ºC? The specific heat capacity of water is 4.2 × 103 J kg–1 K–1; the specific latent heat of fusion is 3.4 × 105 J kg–1.

(4 marks)

6 In a coffee shop, steam at 100 ºC is passed into milk to heat it up and froth it. In this way 100 g milk is heated from 20 ºC to 80 ºC.

Calculate the mass of steam that was condensed into the milk to bring this about. The specific heat capacity of water is 4.2 × 103 J kg–1 K–1, the specific heat capacity of milk is 4.0 × 103 J kg–1 K–1,

and the specific latent heat of vaporisation of water is 2.2 ×

106 J kg–1.

(4 marks)

7 A thermistor has a graph of resistance versus temperature shown in Figure 2.

Figure 2 Graph of resistance versus temperature for a thermistor

(a) Discuss the differences between the behaviour of the thermistor material depicted in this graph and a typical metal as the temperature increases. Include consideration of the

number of charge carriers and the drift velocity of the electrons.

(6 marks) (b) Use the graph to estimate the resistance of the thermistor at

10 ºC and 30 ºC.

(3 marks)

(c) If you were conducting the experiment to measure the resistance as a function of temperature, describe what measures you could take to improve the accuracy.

(3 marks)

(d) The thermistor is placed in a potential divider circuit shown in Figure 3. Calculate V at 10 ºC, using your measurement from (b).

(3 marks)

Figure 3 The circuit for Question 7 Part (d)

8 A tank of volume 0.02 m3 contains 0.20 kg of helium at 27 ºC.

(a) How many moles of helium are present? (hint: the relative

atomic mass in grams is one mole)

(2 marks) (b) Calculate the pressure of the gas in Pa. The universal molar

gas constant R = 8.31 J K–1 mol–1

(3 marks)

9

(a) State three assumptions in kinetic theory of gases.

(3 marks)

(b) Use a simple model: a total of N molecules are contained in a box of side length d. Each molecule has a mass m and a velocity u. By considering the collisions between the molecules and the walls of the box, using the assumptions stated in part (a), derive the equation: pV = ? N m c2

where p is the pressure of the gas, V is its volume and c2 is

the mean square speed of the gas. Ensure that you explain your working and show every step. (6 marks)

(c) Five molecules have the following speeds in m s–1:

473, 482, 517, 490, 501.

Calculate their root mean square speed.

(3 marks)

(d) By combining the result from part (b) with pV = NkT, derive the equation:

(3 marks)

(e) A helium atom has a mass of 6.7 × 10–27 kg. If a sample of gas has a root mean square speed of 500 m s–1, calculate the temperature of the gas.

(3 marks)

10 A pump is being used to inflate a bicycle tyre. The radius of the wheel to the centre of the tyre is 30 cm, and the mean radius of the tyre is 1.5 cm. This is illustrated in Figure 4.

Figure 4 The bicycle tyre

(a) Estimate the volume of the tyre in m3 (hint: to a first approximation you can take the cross-sectional area of the tyre and multiply by the mean circumference of the wheel).

(4 marks)

(b) The tyre starts out completely deflated (i.e. there is no air in it). A pump is being used to inflate it which has a stroke volume of 8 × 10–5 m3. The final pressure inside the tyre is to be 2 × 105 Pa, and the air pressure is 1.01 × 105 Pa. Calculate the number of strokes that will be needed. Assume that this will be done slowly to avoid heating up the air.

(4 marks)

(c) Explain why, in practice, the pump will generally get hot when pumping up a tyre. (2 marks)

Total for assignment 60 marks

Submit your assignment

When you have completed your assignment, submit it to your tutor for marking. Please use pdf format. Your tutor will send you helpful feedback and advice to help you progress through the course.

Thermodynamics

Introduction

Aims

This assignment will test your ability to: ? answer multiple-choice questions ? describe practical situations and interpret measurements.

You do not need to have studied the physics that underlies these experiments in order to be able to complete the tasks.

Links to the assessment requirements

The assessment objectives for the A level that are relevant to this assignment are to:

n apply knowledge and understanding of scientific ideas,

processes, techniques and procedures: ? in a practical context ? when handling qualitative data ? when handling quantitative data

n analyse, interpret and evaluate scientific information, ideas and evidence, including in relation to issues, to: ? make judgements and reach conclusions ? develop and refine practical design and procedures.

How your tutor will mark your work

Your tutor will assess the following aspects of your work: ? your application of appropriate physical principles ? your use of appropriate equations ? the accuracy of your calculations ? your use of graphs and drawings where directed ? your use of appropriate units.

Are you ready to do this assignment?

Before you tackle this assignment, ensure that you have studied Section 9 of the course and Chapters 10, 11 and 12 of the textbook. In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler and protractor, graph paper and a calculator.

The assignment

In calculations, use g = 9.81 m s–2 for the acceleration of free fall unless told otherwise. Data for other questions can be found in the Data booklet, which is linked to Section 6.

1 Figure 1 shows the variation of temperature with time of a sample of ice, turning into water. In what region(s) do ice and water coexist in equilibrium?

Figure 1 Illustration for Question 1

(a) Between A and B. (b) Between B and C.

(c) Between C and D.

(d) None of these regions. (1 mark)

2 A fixed mass of gas has a volume V. If the temperature is changed such that the root mean square velocity of the molecules of the gas is doubled, while the pressure remains constant, what is the new volume of the gas?

(a) V

(b) 1.4 V

(c) 2 V

(d) 4 V

(1 mark)

3 A volume of gas has a pressure 1.5 × 104 Pa at 0 ºC. If the volume is kept constant, to what temperature must it be heated to reach a pressure of 2.1 × 104 Pa?

(a) 382 K

(b) 164 K

(c) 455 K

(d) 195 K

(1 mark)

4 Which of the following statements correctly describes the energy of water molecules when they are being changed from the solid state to the liquid state at 0 ºC?

(a) The internal energy stays the same.

(b) Their kinetic energy is increasing.

(c) Their internal energy falls.

(d) Their kinetic energy stays the same.

(1 mark)

5 50 g of water at 40 ºC is placed in a well-insulated container. Neglecting heat losses, what mass of ice at 0 ºC must be added to reduce the temperature of the water to 12 ºC? The specific heat capacity of water is 4.2 × 103 J kg–1 K–1; the specific latent heat of fusion is 3.4 × 105 J kg–1.

(4 marks)

6 In a coffee shop, steam at 100 ºC is passed into milk to heat it up and froth it. In this way 100 g milk is heated from 20 ºC to 80 ºC.

Calculate the mass of steam that was condensed into the milk to bring this about. The specific heat capacity of water is 4.2 × 103 J kg–1 K–1, the specific heat capacity of milk is 4.0 × 103 J kg–1 K–1,

and the specific latent heat of vaporisation of water is 2.2 ×

106 J kg–1.

(4 marks)

7 A thermistor has a graph of resistance versus temperature shown in Figure 2.

Figure 2 Graph of resistance versus temperature for a thermistor

(a) Discuss the differences between the behaviour of the thermistor material depicted in this graph and a typical metal as the temperature increases. Include consideration of the

number of charge carriers and the drift velocity of the electrons.

(6 marks) (b) Use the graph to estimate the resistance of the thermistor at

10 ºC and 30 ºC.

(3 marks)

(c) If you were conducting the experiment to measure the resistance as a function of temperature, describe what measures you could take to improve the accuracy.

(3 marks)

(d) The thermistor is placed in a potential divider circuit shown in Figure 3. Calculate V at 10 ºC, using your measurement from (b).

(3 marks)

Figure 3 The circuit for Question 7 Part (d)

8 A tank of volume 0.02 m3 contains 0.20 kg of helium at 27 ºC.

(a) How many moles of helium are present? (hint: the relative

atomic mass in grams is one mole)

(2 marks) (b) Calculate the pressure of the gas in Pa. The universal molar

gas constant R = 8.31 J K–1 mol–1

(3 marks)

9

(a) State three assumptions in kinetic theory of gases.

(3 marks)

(b) Use a simple model: a total of N molecules are contained in a box of side length d. Each molecule has a mass m and a velocity u. By considering the collisions between the molecules and the walls of the box, using the assumptions stated in part (a), derive the equation: pV = ? N m c2

where p is the pressure of the gas, V is its volume and c2 is

the mean square speed of the gas. Ensure that you explain your working and show every step. (6 marks)

(c) Five molecules have the following speeds in m s–1:

473, 482, 517, 490, 501.

Calculate their root mean square speed.

(3 marks)

(d) By combining the result from part (b) with pV = NkT, derive the equation:

(3 marks)

(e) A helium atom has a mass of 6.7 × 10–27 kg. If a sample of gas has a root mean square speed of 500 m s–1, calculate the temperature of the gas.

(3 marks)

10 A pump is being used to inflate a bicycle tyre. The radius of the wheel to the centre of the tyre is 30 cm, and the mean radius of the tyre is 1.5 cm. This is illustrated in Figure 4.

Figure 4 The bicycle tyre

(a) Estimate the volume of the tyre in m3 (hint: to a first approximation you can take the cross-sectional area of the tyre and multiply by the mean circumference of the wheel).

(4 marks)

(b) The tyre starts out completely deflated (i.e. there is no air in it). A pump is being used to inflate it which has a stroke volume of 8 × 10–5 m3. The final pressure inside the tyre is to be 2 × 105 Pa, and the air pressure is 1.01 × 105 Pa. Calculate the number of strokes that will be needed. Assume that this will be done slowly to avoid heating up the air.

(4 marks)

(c) Explain why, in practice, the pump will generally get hot when pumping up a tyre. (2 marks)

Total for assignment 60 marks

Submit your assignment

When you have completed your assignment, submit it to your tutor for marking. Please use pdf format. Your tutor will send you helpful feedback and advice to help you progress through the course.

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