Definitions [8]
Define mean free path and write down its expression.
The average distance travelled by the molecule between collisions is called mean free path (λ).
λ = `"kT"/(sqrt(2)π"d"^2"p")`
Define the term degrees of freedom.
The minimum number of independent coordinates needed to specify the position and configuration of a thermo-dynamical system in space is called the degree of freedom of the system.
Thermal equilibrium is the physical state of two bodies when they are connected by a permeable path, don’t undergo any heat transfer and both the bodies have the same temperature.
Define heat engine.
Heat engine is a device which takes heat as input and converts this heat into work by undergoing a cyclic process.
"Temperature is a physical quantity that defines the thermodynamic state of a system."
Define one mole.
One mole of any substance is the amount of that substance which contains the Avogadro number (NA) of particles (such as atoms or molecules).
"Heat is energy in transit. When two bodies at different temperatures are brought in contact, they exchange heat."
Define 'Greenhouse effect'.
The heating-up of the earth’s atmosphere due to trapped infrared rays reflected from the earth's surface by atmospheric gases is called the greenhouse effect.
Formulae [3]
Write the mathematical equation of the first law of thermodynamics for an isochoric process.
By substituting equation W = −pex . ΔV in the equation ΔU = q + W, we get
ΔU = q − pex . ΔV ...(1)
If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.
The equation (1) becomes ΔU = qv
Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.
\[E_k=\frac{3}{2}k_BT\]
Where:
- Ek = Average kinetic energy of the molecules (in joules)
- kB = Boltzmann constant = 1.380649 × 10−23 J/K
- T = Absolute temperature (in kelvin)
Q = mcΔT
Where:
- Q = Heat absorbed or released (in joules)
- m = Mass of the substance (in kg)
- c = Specific heat capacity (J/kg·K)
- ΔT = Change in temperature (Tfinal−Tinitial)
Theorems and Laws [1]
Write the mathematical equation of the first law of thermodynamics for an isochoric process.
By substituting equation W = −pex . ΔV in the equation ΔU = q + W, we get
ΔU = q − pex . ΔV ...(1)
If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.
The equation (1) becomes ΔU = qv
Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.
Important Questions [38]
- Prove that Root Mean Square Velocity of Gas Molecule is Directly Proportional to the Square Root of Its Absolute Temperature.
- State Any Four Assumptions of Kinetic Theory of Gases.
- Show that R.M.S. Velocity of Gas Molecules is Directly Proportional to Square Root of Its Absolute Temperature.
- If the Total Kinetic Energy per Unit Volume of Gas Enclosed in a Container is E, the Pressure Exerted by the Gas is
- At what temperature will average kinetic energy of gas be exactly half of its value at N.T.P.?
- Choose the correct option. The mean free path λ of molecules is given by where n is the number of molecules per unit volume and d is the diameter of the molecules.
- Two Gases Exert Pressure in the Ratio 3: 2 and Their Densities Are in the Ratio 2: 3, Then the Ratio of Their R.M.S. Velocities is
- Derive the ratio of two specific heat capacities of monoatomic, diatomic and triatomic molecules.
- A Body Cools at the Rate of 0.5°C / Minute When It is 25° C Above the Surroundings. Calculate the Rate of Cooling When It is 15°C Above the Same Surroundings.
- An ideal monoatomic gas is adiabatically compressed so that its final temperature is twice its initial temperature. What is the ratio of the final pressure to its initial pressure?
- Draw a p-V diagram and explain the concept of positive and negative work. Give one example each.
- The dimensions of emissive power are ______.
- The light from the Sun is found to have a maximum intensity near the wavelength of 470 nm. Assuming the surface of the Sun as a black body, the temperature of the Sun is _____________.
- Compute the Temperature at Which the R.M.S. Speed of Nitrogen Molecules is 832 M/S.
- Define Emissive Power and Coefficient of Emmision of a Body.
- Two Copper Spheres of Radii 6 Cm and 12 Cm Respectively Are Suspended in an Evacuated Enclosure. Each of Them Are at a Temperature 15°C Above the Surroundings. the Ratio of Their Rate of Loss of Heat is
- A metal sphere cools at the rate of 4°C / min. when its temperature is 50°C. Find its rate of cooling at 45°C if the temperature of surroundings is 25°C.
- A Body Cools from 62°C to 54°C in 10 Minutes and to 48°C in the Next 10 Minutes. Find the Temperature of the Surroundings.
- The Susceptibility of Magnesium at 300k is 1.2 X 10-5. at What Temperature Will the Susceptibility Increase to 1.8 X 10-5
- The Substance Which Allows Heat Radiations to Pass Through is _______.
- The Kinetic Energy per Molecule of a Gs at Temperature T is _______
- A Body Cools from 80° C to 70° C in 5 Minutes and to 62° C in the Next 5 Minutes. Calculate the Temperature of the Surroundings.
- A Metal Ball Cools from 64 °C to 50 °C in 10 Minutes and to 42 °C in Next 10 Minutes. the Ratio of Rates of Fall of Temperature During the Two Intervals is _______.
- At What Temperature Will the Susceptibility of Magnesium Increase
- A Pinhole is Made in a Hollow Sphere of Radius 5 Cm Whose Inner Wall is at Temperature 727 C. Find the Power Radiated per Unit Area.
- 1000 Tiny Mercury Droplets Coalesce to Form a Bigger Drop. in this Process, Temperature of The Drop
- What is the Wavelength Range of Thermal Radiation
- Explain Black Body Radiation Spectrum in Terms of Wavelength
- What is Perfectly Black Body ? Explain Ferry’S Black Body.
- The Wavelength of Emitted Radiation
- Find the Wavelength at Which a Black Body Radiates Maximum Energy, If Its Temperature is 427°C.
- Draw a Neat Labelled Diagram for Ferry'S Perfectly Black Body.
- Show Graphical Representation of Energy Distribution Spectrum of Perfectly Black Body.
- What Happen If the Wavelength Of Incident Radiation is Increased
- State Wein'S Displacement Law
- Explain Maxwell Distribution of Molecular Speed with Necessary Graph.
- The Specific Heat Capacity of Water is
- What is the Ratio of Two Specific Heats,Cp/Cv ?
Concepts [17]
- Concept of an Ideal Gas
- Assumptions of Kinetic Theory of Gases
- Mean Free Path
- Derivation for Pressure of a Gas
- Degrees of Freedom
- Derivation of Boyle’s Law
- Thermal Equilibrium
- First Law of Thermodynamics
- Heat Engine
- Temperature and Heat
- Qualitative Ideas of Black Body Radiation
- Wien's Displacement Law
- Green House Effect
- Stefan's Law
- Maxwell Distribution
- Specific Heat Capacities - Gases
- Law of Equipartition of Energy
