Molecular Theory of gases - Physics II - For HSC Part 2 / XII / Class 12 (Science Group) -Short Question Answers- Section B - CRQs And Self Assessment Questions

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Unit 15: Molecular Theory of gases
Physics II -
For HSC Part 2 / XII / Class 12 (Science Group)

• Section B-CRQs
• Self Assessment Questions

SECTION B
CRQs (Constructed Response Questions)
OR Short Answered Questions)

Q.1: Why the earth is not in thermal equilibrium with the sun?
Ans: The Earth is not in thermal equilibrium with the Sun because it continuously receives energy from the Sun in the form of solar radiation. This energy heats the Earth's surface, causing temperature variations and weather phenomena. Additionally, the Earth radiates energy back into space, creating a dynamic balance rather than a static equilibrium.

OR

Ans: Earth and sun are not in equilibrium because they don't form an isolated system.

Q.2: Describe the relationship between temperature and kinetic energy of molecules.
Ans: Temperature is a measure of the average kinetic energy of the molecules in a substance. As the temperature increases, the kinetic energy of the molecules also increases, leading to faster movement and more vigorous collisions among them. Conversely, a decrease in temperature results in lower kinetic energy and slower molecular motion.

OR

Ans: The relationship between temperature and the kinetic energy of molecules is direct and proportional. As the temperature of a substance increases, the average kinetic energy of its molecules also increases. This means that at higher temperatures, molecules move faster, and at lower temperatures, they move more slowly. Temperature is essentially a measure of the average kinetic energy of the molecules in a substance.

Q.3: It is observed that when mercury in glass thermometer is put in a flame, the column of mercury first descends and then rises. Explain.
Ans: When the thermometer is first heated, the gas expands more quickly than the mercury, causing the mercury to descend initially. As the temperature continues to rise, the mercury eventually expands and rises in the tube as it absorbs heat. This phenomenon is due to the different thermal expansion properties of glass and mercury.

OR

Ans: Due to expansion of the glass, mercury first falls but later on rises due to larger coefficient of expansion for mercury than that of glass.

Q.4: What is standard temperature, pressure?
Ans: Standard temperature and pressure (STP) are defined as a temperature of 0 degra Celsius (273.15 K) and a pressure of 1 atmosphere (101.325 kPa). These conditions are used as reference points for various scientific calculations and experiments.

OR

Ans: Standard temperature and pressure (STP) refers to the nominal conditions in the atmosphere at sea level. These conditions are 0 degrees Celsius (273.15 K) and 1 atmosphere (atm) (101.325 kPa) of pressure.

Q.5: A thermometer is placed in direct sun light. What will it read the temperature?
Ans: A thermometer placed in direct sunlight may read a high temperature than the actual air temperature due to the heat absorbed from solar radiation. The reading can be influenced by factors such as the type of thermometer, its material, and exposure time.

OR

Ans: If a thermometer is placed in direct sun light, it will measure a much higher temperature than that of the air.

Q.6: The pressure in a gas cylinder containing hydrogen will leak more quickly than if it is containing oxygen. Why?
Ans: Hydrogen molecules are lighter and smaller than oxygen molecules, allowing them to move faster and escape through tiny openings more easily. This phenomenon is described by Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

OR

Ans: As the hydrogen is lighter than oxygen i.e., its molecular mass and density is less than that of oxygen therefore rate of diffusion of hydrogen gas is greater than oxygen. That is why the pressure in a gas cylinder containing hydrogen will leak more quickly than the gas cylinder containing oxygen.

Q.7: When a sealed thermos bottle full of coffee is shaken, what are the changes occur?
Ans: Shaking a sealed thermos bottle full of coffee increases the kinetic energy of the coffee molecules leading to a rise in temperature The agitation can also cause the coffee to mix more thoroughly, but since the thermos is insulated there will be minimal heat loss to the environment.

OR

Ans: When the bottle is shaken, the coffee will experience some internal movement, which may cause some molecules to collide and exchange kinetic energy. However, this effect is small, and the overall temperature of the coffee will remain nearly constant.

Q.8: How does the Kinetic theory account for the following observed facts:
(a) A gas exerts pressure
(b) The pressure of a gas depends upon its temperature.
Ans: a) A gas exerts Pressure:
According the kinetic theory, gas consists of a large number of small particles (molecules) that are in constant random motion. As these molecules collide with the walls of their container, they exert force on the walls. The cumulative effects of countless collisions results in pressure exerted by th gas. The more frequent and forceful the collisions, the higher the pressure.

b) The pressure of gas depends upon its temperature:
The kinetic theory states that the temperature of a gas is a measure of the average kinetic energy of its molecules. As the temperature increases, the kinetic energy of the molecules increases, causing them to move faster. This results in more frequent and more forceful collisions with the walls of the container, leading to an increase in pressure. Conversely lowering the temperature decreases the kinetic energy, resulting in lower pressure.

OR

Ans: The Kinetic Theory explains the behavior of gases through the motion of their particles:
(a) A gas exerts pressure:
According to the Kinetic Theory, gas particles are in constant random motion. When these particles collide with the walls of a container, they exert a force on the walls. The collective force of these collisions per unit area is what we observe as gas pressure.

(b) The pressure of a gas depends upon its temperature:
The temperature of a gas is a measure of the average kinetic energy of its particles. As the temperature increases, the particles move faster, resulting in more frequent and forceful collision with the container walls. This increase in the frequency and intensity of collisions leads to an increase i n pressure.

Q.9: Calculate the average speed of an air molecule at room temperature (20°C) and compare it to the speed of sound in air (330 m/s).
Ans: CALCULATION:
First, we need to calculate the average speed of an air molecule at room temperature.
FORMULA:
The average speed of a gas molecule can be calculated using the formula:

Where:

• K is the Kinetic energy
• k is the Boltzmann constant, approximately 1.38 x 10^-23 J/K
• T is the absolute temperature in Kelvin,
• m is the mass of a gas molecule.
  The average molar mass of air is approximately 29 g/m.
  For the mass of a single molecule. we convert this to kilograms and then divide it by Avogadro's number (6.023 x 10^-23)
  Mass of a gas molecule (m) = 29 / 1000 = 0.029 = 29 x 10^-3 Kg/ mole
  
  
• v_avg is the average speed of an air molecule
  

DATA:
T = 20 °C + 273 = 293 K
k = 1.38 x 10^-23 J/K
m = 4.82 x 10^-26 Kg
V_avg = ?

SOLUTION:

COMPARISON:
The average speed in air molecule at room temperate (20°C) is approximately 501.70 m/s, which is significantly higher than the speed of sound in air (330 m/s). This indicates that while individual molecules at high speed moving at high speeds, the collective behavior of these molecules results in sound propagation at a lower due to the interactions and compressibility of the gas.

OR

The average speed of the air molecule (501 m/s) is greater than the speed of sound in air (330 m/s)

OR

In comparison, molecule of air is moving faster than sound because V_avg = 501.70 m/s > V_sound = 330 m/s.

More Short Answered Questions

Q.10: How does Thermometer device help to measure the temperature of any other body? OR Define thermal equilibrium? OR What is the principle of thermometer?
Ans: PRINCIPLE OF THERMOMETER OR THERMAL EQUILIBRIUM:
Thermometer works on the principle of thermal equilibrium. When two bodies at different temperatures are brought in thermal contact with each other, the heat start flowing from the hot body to the cold body till the temperature of both bodies becomes same then they are said to be in thermal equilibrium.

Q.11: What do you mean by gas law
Ans: GAS LAW:
An interrelation among the physical quantities of a given sample of gas which determine the state of a gas is termed as "equation of state" of gas or Gas Laws.
These physical quantities are:

• Pressure (P)
• Volume (V)
• Temperature (T)
• Mass (m)

There are following gas laws:

• Boyle's law
• Charle's law
• Avogadro's law
• General gas equation

Q.12: What is critical point? Also define critical pressure and critical temperature?

Ans: CRITICAL POINT:
Liquid vapor equilibrium region" corresponds to the end point at the top of vaporization curve, it is called critical point and the corresponding values of P and T are called critical pressure P_C, and temperature T_C.

Critical Pressure:
Critical pressure is a liquid vapor pressure at critical temperature, where liquid and gas coexist, forming one phase..

Critical Pressure:
The critical temperature for a pure substance is the temperature above which the gas cannot become liquid, regardless of the applied pressure. A gas above the critical temperature does not separate into phases when it is compressed isothermally.

Q.13: Define Absolute zaro, Avogaro's number, real or permanent gas and ideal or perfect gas?
Ans: Absolute Zero: The temperature at which volume of a gas becomes zero and molecular motion ceases is termed as absolute zero. Kelvin selected value of this temperature as -273.15 °C on Centigrade temperature scale, −459.67 °F on the Fahrenheit temperature scale and 0K on Kelvin temperature scale

Avogadro's Number:
A mole of any substance is that mass of substance that contains a specific Number of molecules called Avogadro's number. It is represented by N_A. NA = 6.022 x 10²³ molecules/mole.
Avogadro's number is defined to be the number of carbon atoms in 12g of the isotope carbon-12. The number of moles of a substance is related to its m mass m.i.e.:
n = ^m/_M
Where M is the molecular mass of the substance usually expressed in g/mole.

Real or Permanent Gas
Real or permanent gas is a gas that obeys gas Laws at high temperature and low Pressure only.

Ideal or Perfect gas
Ideal or perfect gas is a gas that obeys gas Laws at all temperatures and pressures.

Q.14: What are K and R constant?
Ans: k Constant:
K (Boltzmann constant) is universal gas constant per molecule of a gas. Its value is 1.38 J/Molecula k.

R constant:
R is a universal gas Constant per mole of gas. Its value is 8.314 J^-1K^-1.

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SELF ASSESSMENT QUESTIONS

1. Convert each of the following temperature from the centigrade scale to Kelvin scale and Fahrenheit 0°C, 20°C, 120°C, 500°C, —23°C, 200°C.
Ans: Centigrade (Celsius) To Kelvin Scale:
FORMULA:

T_K = T_°C + 273

i) 0 °C
Solution:
T_K = T_°C + 273
⇒ T_K = 0 + 273 = 273 K Ans.

ii) 20 °C
Solution:
T_K = T_°C + 273
⇒ T_K = 20 + 273 = 293 K Ans.

iii) 120 °C
Solution:
T_K = T_°C + 273
⇒ T_K = 120 + 273 = 393 K Ans.

iv) 500 °C
Solution:
T_K = T_°C + 273
⇒ T_K = 500 + 273 = 773 K Ans.

v) -23 °C
Solution:
T_K = T_°C + 273
⇒ T_K = -23 + 273 = 250 K Ans.

vi) 200 °C
Solution:
T_K = T_°C + 273
⇒ T_K = 200 + 273 = 493 K Ans.

Centigrade (Celsius) To Fahrenheit Scale:

2. Convert each of the following temperature from the Kelvin scale to the Celsius scale and Fahrenheit O K, 20 K, 100 K, 300 K, 373 K, and 500 K.
Ans: Kelvin Scale To Centigrade (Celsius):
FORMULA:

T_°C = T_K - 273

i) 0 K
Solution:
T_°C = T_K - 273
⇒ T_°C = 0 - 273 = -273 °C Ans.

ii) 20 K
Solution:
T_°C = T_K - 273
⇒ T_°C = 20 - 273 = -253 °C Ans.

iii) 100 K
Solution:
T_°C = T_K - 273
⇒ T_°C = 100 - 273 = -173 °C Ans.

iv) 300 K
Solution:
T_°C = T_K - 273
⇒ T_°C = 300 - 273 = 27 °C Ans.

v) 373 K
Solution:
T_°C = T_K - 273
⇒ T_°C = 373 - 273 = 100 °C Ans.

vi) 500 K
Solution:
T_°C = T_K - 273
⇒ T_°C = 500 - 273 = 227 °C Ans.

Kelvin Scale To Fahrenheit:

i) 0 K
Solution:
T_°F = 1.8 (T_K - 273) + 32
⇒ T_°F = 1.8 (0 - 273) + 32
⇒ T_°F = 1.8 (-273) + 32 ⇒ T_°F = - 491.4 + 32 = -459.4 °F Ans.

ii) 20 K
Solution:
T_°F = 1.8 (T_K - 273) + 32
⇒ T_°F = 1.8 (20 - 273) + 32
⇒ T_°F = 1.8 (-253) + 32 ⇒ T_°F = - 455.4 + 32 = -423.4 °F Ans.

iii) 100 K
Solution:
T_°F = 1.8 (T_K - 273) + 32
⇒ T_°F = 1.8 (100 - 273) + 32
⇒ T_°F = 1.8 (-173) + 32 ⇒ T_°F = - 311.4 + 32 = -279.4 °F Ans.

iv) 300 K
Solution:
T_°F = 1.8 (T_K - 273) + 32
⇒ T_°F = 1.8 (300 - 273) + 32
⇒ T_°F = 1.8 (27) + 32 ⇒ T_°F = - 48.6 + 32 = 80.6 °F Ans.

v) 373 K
Solution:
T_°F = 1.8 (T_K - 273) + 32
⇒ T_°F = 1.8 (373 - 273) + 32
⇒ T_°F = 1.8 (100) + 32 ⇒ T_°F = 180 + 32 = 212 °F Ans.

vi) 500 K
Solution:
T_°F = 1.8 (T_K - 273) + 32
⇒ T_°F = 1.8 (500 - 273) + 32
⇒ T_°F = 1.8 (227) + 32 ⇒ T_°F = 408.6 + 32 = 440.6 °F Ans.

3. What are the conditions (temperature and pressure) at which the triple point of water occurs?
Ans: Triple Point Of Water:
The triple point of water occurs at a temperature of 273.16 K (0.01°C) and a pressure of 4.58 mm of mercury or 611.73 Pascal.

4. Where is the triple point located in relation to the solid, liquid, and gas regions?
Ans: Location Of Triple Point Of Water:
The triple point is located at the intersection where the lines separating the solid, liquid, and gas phases meet on the phase diagram. It is the point where all three phases coexist in thermodynamic equilibrium.

5. How does the pressure of a gas change if its volume is halved at constant temperature?
Ans: According to Boyle's Law, at constant temperature, the pressure of a gas is inversely proportional to its volume. Therefore, if the volume is halved, the pressure will double.

6. What happens to the volume of a gas when its temperature is increased while keeping the pressure constant?
Ans: According to Charles's Law, at constant pressure, the volume of a gas is directly proportional to its temperature (measured in Kelvin). So, increasing the temperature will cause the volume to increase.

7. What is the relationship between the volume and the number of moles of a gas at constant temperature and pressure?
Ans: According to Avogadro's Law, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. Increasing the number of moles will increase the volume proportionally.

8. Describe the motion of molecules in a gas according to the kinetic molecular theory.
Ans: According to the kinetic molecular theory, molecules in a gas move in all directions with a wide range of speeds. They are in constant, random motion, colliding elastically with each other and with the walls of the container. These collisions are perfectly elastic, meaning there is no loss of kinetic energy during collisions, and molecules move freely in straight lines between collisions.

9. What is the relationship between temperature and molecular motion in a gas?
The temperature of a gas is directly related to the average kinetic energy of its molecules. As temperature increases, the molecules move faster, resulting in higher average kinetic energy. Conversely, lowering the temperature decreases the molecular speed and kinetic energy.