Thermal

Flashcard 1

Front: What is internal energy?

Back:

●

The internal energy of a body is the sum of the kinetic and potential energies of all its particles1.

●

These energies are randomly distributed1.

Flashcard 2

Front: What are the two ways to increase the internal energy of a system?

Back:

●

Do work on the system, for example, by moving its particles or changing its shape1.

●

Increase the temperature of the system2.

Flashcard 3

Front: How does the internal energy of a substance change when its state changes?

Back:

●

The internal energy changes because the potential energy of the system changes, while the kinetic energy remains constant2.

●

For example, when water boils, the energy gained through heating is used to break the bonds between water molecules so that it can change state to water vapour. This increases the potential energy2.

Flashcard 4

Front: What formula can you use to calculate the amount of energy required to change the temperature of a substance?

Back:

●

Q = m*c*Δθ3

●

Where:

○

Q = energy required

○

m = mass

○

c = specific heat capacity

○

Δθ = change in temperature

Flashcard 5

Front: What is specific heat capacity?

Back:

●

The specific heat capacity of a substance is the amount of energy required to increase the temperature of 1 kg of the substance by 1 °C or 1 K without changing its state3.

Flashcard 6

Front: What formula can you use to calculate the amount of energy required to change the state of a substance?

Back:

●

Q = m*l4

●

Where:

○

Q = energy required

○

m = mass

○

l = specific latent heat

Flashcard 7

Front: What is specific latent heat? What are the two types of specific latent heat?

Back:

●

Specific latent heat is the amount of energy required to change the state of 1 kg of a material, without changing its temperature4.

●

The two types are:

○

Specific latent heat of fusion: When a solid changes to a liquid4

○

Specific latent heat of vaporisation: When a liquid changes to a gas4

Flashcard 8

Front: A kettle has a power of 1200 W and contains 0.5 kg of water at 22°C. How long will it take for the water in the kettle to reach 100°C? (Specific heat capacity of water = 4200 J/kg°C)

Back:

Calculate the energy (Q) required to increase the temperature of the water to 100 °C using the formula Q = m*c*Δθ4.

Calculate the time (t) taken using the formula t = Q/P, where P is the power of the kettle5.

The answer is 136.5 s5.

Flashcard 9

Front: An ice cube with a mass of 0.01 kg at a temperature of 0°C is dropped into a glass of water with a mass of 0.2 kg at a temperature of 19°C. What is the final temperature of the water once the ice cube has fully melted? (Specific heat capacity of water = 4200 J/kg°C, specific latent heat of fusion of ice = 334,000 J/kg).

Back:

Calculate the energy (Q) required to change the state of the ice using the formula Q = m*l6.

Set up a pair of simultaneous equations to show the energy transfer in the water and the ice separately. The energy transfer is the same in both because the system is closed. You can equate these values to find the final temperature (T)6.

○

For ice: Q = m*l + m*c*Δθ (because the ice changes state and temperature)6

○

For water: Q = m*c*Δθ6

Solve the simultaneous equations to find T.

The answer is 14.3°C7.

Flashcard 10

Front: Water flows past an electric heater with a power of 9000 W at a rate of 0.5 kg/s. What is the increase in temperature of the water per second that it flows past the heater? (Specific heat capacity of water = 4200 J/kg°C).

Back:

9000 J of energy are transferred every second because the power of the heater is 9000 W. 0.5 kg of water flows past the heater every second8.

Use the formula Δθ = Q/(m*c) to find the increase in temperature8.

The answer is 4.3°C8.

Ideal Gases

Flashcard 11

Front: What are the gas laws?

Back:

●

The gas laws describe the experimental relationship between pressure (p), volume (V), and temperature (T) for a fixed mass of gas8.

●

They are empirical in nature. This means they are not based on theory but arose from observation and experimental evidence8.

●

The three gas laws you need to be aware of are:

Boyle's Law: When the temperature is constant, the pressure and volume are inversely proportional8.

Charles' Law: When the pressure is constant, the volume is directly proportional to absolute temperature8.

The Pressure Law: When the volume is constant, the pressure is directly proportional to the absolute temperature9.

Flashcard 12

Front: What is the absolute scale of temperature?

Back:

●

The absolute scale of temperature is the Kelvin scale9.

●

All equations in thermal physics use temperatures measured in Kelvin (K)9.

●

A change of 1 K is equal to a change of 1°C9.

Flashcard 13

Front: How do you convert between Celsius and Kelvin?

Back:

●

K = C + 2739

●

Where:

○

K is the temperature in Kelvin

○

C is the temperature in Celsius

Flashcard 14

Front: What is absolute zero?

Back:

●

Absolute zero (-273°C), also known as 0 K, is the lowest possible temperature9.

●

At absolute zero, particles have no kinetic energy, and the volume and pressure of a gas are zero9.

Flashcard 15

Front: What are the combined and ideal gas equations?

Back:

●

The experimental gas laws can be combined into one equation: pV = kT10.

○

The constant k is dependent on the amount of gas used, measured in moles10.

●

This can be rewritten to get the ideal gas equation: pV = nRT10

○

Where:

■

n = the number of moles of gas

■

R = the molar gas constant (8.31 J mol⁻¹ K⁻¹)

Flashcard 16

Front: What is a mole? How can you convert between the number of moles and the number of molecules?

Back:

●

1 mole of a substance is equal to 6.02 × 10²³ atoms/molecules11.

●

You can convert between the number of moles (n) and the number of molecules (N) by multiplying the number of moles by 6.02 × 10²³, which is defined as the Avogadro constant (NA)11.

●

N = n × NA ⇒ n = N/NA11

Flashcard 17

Front: What is the formula for the ideal gas equation in terms of the number of molecules?

Back:

●

You can substitute n = N/NA into the ideal gas equation (pV = nRT) to get it in terms of molecules: pV = (N*R*T)/NA11.

●

This can be simplified using the Boltzmann constant (k), which is equivalent to R/NA: pV = N*k*T11.

Flashcard 18

Front: What is molar mass? How can it be found?

Back:

●

Molar mass is the mass (in grams) of one mole of a substance12.

●

It can be found by finding the relative molecular mass, which is (approximately) equal to the sum of the nucleons in a molecule of the substance12.

Flashcard 19

Front: How do you calculate the work done on a gas to change its volume at a constant pressure?

Back:

●

Work is done on a gas to change its volume when it is at constant pressure. This is usually done through the transfer of thermal energy. The formula for work done is: W = p*ΔV12

●

Where:

○

p = pressure

○

ΔV = the change in volume

●

When working with a graph of pressure against volume, the work done is the area under the graph12.

Molecular Kinetic Theory Model

Flashcard 20

Front: What is Brownian motion?

Back:

●

Brownian motion is the random motion of larger particles in a fluid caused by collisions with surrounding particles13.

●

It can be observed by looking at smoke particles under a microscope13.

●

Brownian motion provided evidence for the existence of atoms and molecules13.

Flashcard 21

Front: How does the simple molecular model explain each of the gas laws?

Back:

●

Boyle's law: If you increase the volume of a fixed mass of gas, the molecules move further apart, so collisions become less frequent, leading to a decrease in pressure13.

●

Charles's law: When the temperature of a gas increases, its molecules gain kinetic energy and move more quickly. Because pressure is kept constant (meaning the frequency of collisions is constant), the molecules move further apart and the volume increases13.

●

Pressure Law: When the temperature of a gas increases, its molecules gain kinetic energy and move more quickly. Because volume is constant, the frequency of collisions between molecules and their container increases and they collide at higher speeds. This leads to increased pressure14.

Flashcard 22

Front: What is the kinetic theory model?

Back:

●

The gas laws are empirical in nature. This means they are not based on theory but arose from observation and experimental evidence. However, the kinetic theory model is the opposite: it arose solely from theory14.

●

The kinetic theory model equation relates several features of a fixed mass of gas, including its pressure, volume and mean kinetic energy14.

Flashcard 23

Front: What are the assumptions of the kinetic theory model?

Back:

No intermolecular forces act on the molecules15.

The duration of collisions is negligible compared to the time between collisions15.

The motion of the molecules is random, and they experience perfectly elastic collisions15.

The motion of the molecules follows Newton’s laws15.

The molecules move in straight lines between collisions15.

Flashcard 24

Front: What is the derivation of the kinetic theory model equation?

Back:

Consider a cube with side lengths l, full of gas molecules. A molecule of mass m is travelling towards the right-most wall of the container with a velocity u. Assuming it collides with the wall elastically, its change in momentum is: m(-u) - mu = 2mu15.

The molecule must travel a distance of 2l before it can collide with the wall again. The time between collisions (t) is therefore: t = 2l/u16.

You can then use this information to find the impulse. Impulse is the rate of change of momentum of the molecule. Impulse is equal to force. Divide the value of impulse by the area of one wall to find pressure: P = mu²/l³ = mu²/V16. This equation can be simplified because l³ is equal to the cube's volume (V)17.

The total pressure of the gas is the sum of all the individual pressures caused by each molecule: P = m((u₁)² + (u₂)² +...+(uₙ)²)/V17.

Instead of considering all of these speeds separately, you can define a quantity known as the mean square speed. This is the mean of the square speeds of the gas molecules. This quantity is written as u² . Multiply it by N, the number of particles in the gas, to get an estimate of the sum of the molecules’ speeds: P = (N*m*u²)/V18.

Now consider all the directions the molecules will be moving in. The particles are moving in all 3 dimensions. Use Pythagoras' theorem to work out the speed the molecules will be travelling at: c² = u² + v² + w², where u, v, and w are the components of the molecule’s velocity in the x, y and z directions18. Because the motion of the particles is random, you can assume the mean square speed in each direction is the same: ∴ u² = v² = w² ⇒ c² = 3u²19.

Substitute this into the equation from step 5 and rearrange: p = (Nm(c²))/3V or p = ⅓Nm(c²)/V19.

c² and (crms)² are equivalent19.

Flashcard 25

Front: What is an ideal gas? What is the internal energy of an ideal gas equal to?

Back:

●

An ideal gas follows the gas laws perfectly. This means there are no other interactions between gas molecules other than perfectly elastic collisions20.

●

This shows that no intermolecular forces act between the molecules20.

●

Because potential energy is associated with intermolecular forces, an ideal gas has no potential energy20.

●

Therefore, its internal energy is equal to the sum of the kinetic energies of all of its particles20.

Flashcard 26

Front: What are the formulas for the kinetic energy of a single gas molecule?

Back:

●

½m(c²)20

●

½m(crms²) = ³/₂kT20

●

³/₂NAkT = ³/₂RT20

Flashcard 27

Front: How does the kinetic energy of a gas molecule relate to temperature?

Back:

●

The kinetic energy of a gas molecule is directly proportional to temperature (in Kelvin)20.

Flashcard 28

Front: A bottle contains 128 g of oxygen at a temperature of 330 K. Find the sum of the kinetic energies of all the oxygen molecules. (Molecular mass of oxygen gas = 32 g)

Back:

Calculate the number of moles using the formula: number of moles = mass/molar mass21.

Multiply this by the Avogadro constant to find the number of molecules21.

Use the formula ³/₂kT to find the kinetic energy of one molecule, then multiply this by the number of molecules to find the sum of the kinetic energies21.

The answer is 6450 J21.

Flashcard 29

Front: How has scientific knowledge and understanding of gases changed over time?

Back:

●

The gas laws were discovered by a number of scientists. They were later explained by the development of the kinetic theory model, which wasn't initially accepted21.

●

Scientific knowledge and understanding of any scientific concept change over time in accordance with the experimental evidence gathered by the scientific community21.Flashcard 1

Front: What is internal energy?

Back:

●

The internal energy of a body is the sum of the kinetic and potential energies of all its particles1.

●

These energies are randomly distributed1.

Flashcard 2

Front: What are the two ways to increase the internal energy of a system?

Back:

●

Do work on the system, for example, by moving its particles or changing its shape1.

●

Increase the temperature of the system2.

Flashcard 3

Front: How does the internal energy of a substance change when its state changes?

Back:

●

The internal energy changes because the potential energy of the system changes, while the kinetic energy remains constant2.

●

For example, when water boils, the energy gained through heating is used to break the bonds between water molecules so that it can change state to water vapour. This increases the potential energy2.

Flashcard 4

Front: What formula can you use to calculate the amount of energy required to change the temperature of a substance?

Back:

●

Q = m*c*Δθ3

●

Where:

○

Q = energy required

○

m = mass

○

c = specific heat capacity

○

Δθ = change in temperature

Flashcard 5

Front: What is specific heat capacity?

Back:

●

The specific heat capacity of a substance is the amount of energy required to increase the temperature of 1 kg of the substance by 1 °C or 1 K without changing its state3.

Flashcard 6

Front: What formula can you use to calculate the amount of energy required to change the state of a substance?

Back:

●

Q = m*l4

●

Where:

○

Q = energy required

○

m = mass

○

l = specific latent heat

Flashcard 7

Front: What is specific latent heat? What are the two types of specific latent heat?

Back:

●

Specific latent heat is the amount of energy required to change the state of 1 kg of a material, without changing its temperature4.

●

The two types are:

○

Specific latent heat of fusion: When a solid changes to a liquid4

○

Specific latent heat of vaporisation: When a liquid changes to a gas4

Flashcard 8

Front: A kettle has a power of 1200 W and contains 0.5 kg of water at 22°C. How long will it take for the water in the kettle to reach 100°C? (Specific heat capacity of water = 4200 J/kg°C)

Back:

Calculate the energy (Q) required to increase the temperature of the water to 100 °C using the formula Q = m*c*Δθ4.

Calculate the time (t) taken using the formula t = Q/P, where P is the power of the kettle5.

The answer is 136.5 s5.

Flashcard 9

Back:

Calculate the energy (Q) required to change the state of the ice using the formula Q = m*l6.

○

For ice: Q = m*l + m*c*Δθ (because the ice changes state and temperature)6

○

For water: Q = m*c*Δθ6

Solve the simultaneous equations to find T.

The answer is 14.3°C7.

Flashcard 10

Back:

9000 J of energy are transferred every second because the power of the heater is 9000 W. 0.5 kg of water flows past the heater every second8.

Use the formula Δθ = Q/(m*c) to find the increase in temperature8.

The answer is 4.3°C8.

Ideal Gases

Flashcard 11

Front: What are the gas laws?

Back:

●

The gas laws describe the experimental relationship between pressure (p), volume (V), and temperature (T) for a fixed mass of gas8.

●

They are empirical in nature. This means they are not based on theory but arose from observation and experimental evidence8.

●

The three gas laws you need to be aware of are:

Boyle's Law: When the temperature is constant, the pressure and volume are inversely proportional8.

Charles' Law: When the pressure is constant, the volume is directly proportional to absolute temperature8.

The Pressure Law: When the volume is constant, the pressure is directly proportional to the absolute temperature9.

Flashcard 12

Front: What is the absolute scale of temperature?

Back:

●

The absolute scale of temperature is the Kelvin scale9.

●

All equations in thermal physics use temperatures measured in Kelvin (K)9.

●

A change of 1 K is equal to a change of 1°C9.

Flashcard 13

Front: How do you convert between Celsius and Kelvin?

Back:

●

K = C + 2739

●

Where:

○

K is the temperature in Kelvin

○

C is the temperature in Celsius

Flashcard 14

Front: What is absolute zero?

Back:

●

Absolute zero (-273°C), also known as 0 K, is the lowest possible temperature9.

●

At absolute zero, particles have no kinetic energy, and the volume and pressure of a gas are zero9.

Flashcard 15

Front: What are the combined and ideal gas equations?

Back:

●

The experimental gas laws can be combined into one equation: pV = kT10.

○

The constant k is dependent on the amount of gas used, measured in moles10.

●

This can be rewritten to get the ideal gas equation: pV = nRT10

○

Where:

■

n = the number of moles of gas

■

R = the molar gas constant (8.31 J mol⁻¹ K⁻¹)

Flashcard 16

Front: What is a mole? How can you convert between the number of moles and the number of molecules?

Back:

●

1 mole of a substance is equal to 6.02 × 10²³ atoms/molecules11.

●

You can convert between the number of moles (n) and the number of molecules (N) by multiplying the number of moles by 6.02 × 10²³, which is defined as the Avogadro constant (NA)11.

●

N = n × NA ⇒ n = N/NA11

Flashcard 17

Front: What is the formula for the ideal gas equation in terms of the number of molecules?

Back:

●

You can substitute n = N/NA into the ideal gas equation (pV = nRT) to get it in terms of molecules: pV = (N*R*T)/NA11.

●

This can be simplified using the Boltzmann constant (k), which is equivalent to R/NA: pV = N*k*T11.

Flashcard 18

Front: What is molar mass? How can it be found?

Back:

●

Molar mass is the mass (in grams) of one mole of a substance12.

●

It can be found by finding the relative molecular mass, which is (approximately) equal to the sum of the nucleons in a molecule of the substance12.

Flashcard 19

Front: How do you calculate the work done on a gas to change its volume at a constant pressure?

Back:

●

Work is done on a gas to change its volume when it is at constant pressure. This is usually done through the transfer of thermal energy. The formula for work done is: W = p*ΔV12

●

Where:

○

p = pressure

○

ΔV = the change in volume

●

When working with a graph of pressure against volume, the work done is the area under the graph12.

Molecular Kinetic Theory Model

Flashcard 20

Front: What is Brownian motion?

Back:

●

Brownian motion is the random motion of larger particles in a fluid caused by collisions with surrounding particles13.

●

It can be observed by looking at smoke particles under a microscope13.

●

Brownian motion provided evidence for the existence of atoms and molecules13.

Flashcard 21

Front: How does the simple molecular model explain each of the gas laws?

Back:

●

Boyle's law: If you increase the volume of a fixed mass of gas, the molecules move further apart, so collisions become less frequent, leading to a decrease in pressure13.

●

Flashcard 22

Front: What is the kinetic theory model?

Back:

●

The kinetic theory model equation relates several features of a fixed mass of gas, including its pressure, volume and mean kinetic energy14.

Flashcard 23

Front: What are the assumptions of the kinetic theory model?

Back:

No intermolecular forces act on the molecules15.

The duration of collisions is negligible compared to the time between collisions15.

The motion of the molecules is random, and they experience perfectly elastic collisions15.

The motion of the molecules follows Newton’s laws15.

The molecules move in straight lines between collisions15.

Flashcard 24

Front: What is the derivation of the kinetic theory model equation?

Back:

The molecule must travel a distance of 2l before it can collide with the wall again. The time between collisions (t) is therefore: t = 2l/u16.

The total pressure of the gas is the sum of all the individual pressures caused by each molecule: P = m((u₁)² + (u₂)² +...+(uₙ)²)/V17.

Substitute this into the equation from step 5 and rearrange: p = (Nm(c²))/3V or p = ⅓Nm(c²)/V19.

c² and (crms)² are equivalent19.

Flashcard 25

Front: What is an ideal gas? What is the internal energy of an ideal gas equal to?

Back:

●

An ideal gas follows the gas laws perfectly. This means there are no other interactions between gas molecules other than perfectly elastic collisions20.

●

This shows that no intermolecular forces act between the molecules20.

●

Because potential energy is associated with intermolecular forces, an ideal gas has no potential energy20.

●

Therefore, its internal energy is equal to the sum of the kinetic energies of all of its particles20.

Flashcard 26

Front: What are the formulas for the kinetic energy of a single gas molecule?

Back:

●

½m(c²)20

●

½m(crms²) = ³/₂kT20

●

³/₂NAkT = ³/₂RT20

Flashcard 27

Front: How does the kinetic energy of a gas molecule relate to temperature?

Back:

●

The kinetic energy of a gas molecule is directly proportional to temperature (in Kelvin)20.

Flashcard 28

Front: A bottle contains 128 g of oxygen at a temperature of 330 K. Find the sum of the kinetic energies of all the oxygen molecules. (Molecular mass of oxygen gas = 32 g)

Back:

Calculate the number of moles using the formula: number of moles = mass/molar mass21.

Multiply this by the Avogadro constant to find the number of molecules21.

Use the formula ³/₂kT to find the kinetic energy of one molecule, then multiply this by the number of molecules to find the sum of the kinetic energies21.

The answer is 6450 J21.

Flashcard 29

Front: How has scientific knowledge and understanding of gases changed over time?

Back:

●

The gas laws were discovered by a number of scientists. They were later explained by the development of the kinetic theory model, which wasn't initially accepted21.

●

Scientific knowledge and understanding of any scientific concept change over time in accordance with the experimental evidence gathered by the scientific community21.