- Temperature: Degree of hotness or coldness of a body. Quantity that determines direction of heat flow.
- Heat: Energy transferred due to temperature difference. It is a form of energy.
- Temperature of system increases if heat is supplied. Decreases if heat is taken out.
- Heat exchange: $Q = mc\Delta T$. ($m$: mass, $c$: specific heat, $\Delta T$: change in temperature).
- SI unit of heat in MKS: Joule (J). In CGS: erg. Thermal unit: calorie.
- $1~\text{calorie} = 4.2~\text{Joule}$.
- Specific Heat: Heat required to raise temperature of unit mass by $1^\circ C$. $c = \frac{Q}{m\Delta T}$.
Temperature & Heat
Thermal Equilibrium & Zeroth Law of Thermodynamics
- If two systems (A and B) are in thermal contact and no net heat flows between them, they are in thermal equilibrium.
- Zeroth Law of Thermodynamics: If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
- Temperature is an intrinsic property of an object.
Conversion Formulas of Temperature Scales
- Celsius to Fahrenheit: $T_F = \frac{9}{5}T_C + 32$.
- Fahrenheit to Celsius: $T_C = \frac{5}{9}(T_F - 32)$.
- Celsius to Kelvin: $T_K = T_C + 273$.
- Kelvin to Celsius: $T_C = T_K - 273$.
- Relation between scales: $\frac{T_C - 0}{100} = \frac{T_F - 32}{180} = \frac{T_K - 273}{100}$.
- Centigrade and Fahrenheit scales show same reading at $-40^\circ$.
- Celsius degree is larger than Fahrenheit degree by a factor of $9/5$.
| Sr. # | Name of scale | Lower Point | Upper Point | Number of divisions |
|---|---|---|---|---|
| 1 | Celsius scale | $0^\circ C$ | $100^\circ C$ | 100 |
| 2 | Fahrenheit scale | $32^\circ F$ | $212^\circ F$ | 180 |
| 3 | Kelvin scale | $273~K$ | $373~K$ | 100 |
Kinetic Molecular Theory of Gases (K.M.T)
- Main points:
- Small volume contains large number of molecules.
- Molecules move randomly and exert no force on one another except during elastic collisions.
- Collisions with walls give rise to gas pressure.
- Gravity does not affect molecular motion.
- Volume of gas molecules is negligible compared to actual volume of gas.
Pressure and Temperature of an Ideal Gas
- Study of microscopic behavior of molecules and their interactions.
- Applying Newton's law to an ideal gas under assumptions of KMT:
- Average force on container walls: $F_{average} = \frac{mN\bar{v^2}}{L}$.
- Pressure: $P = \frac{2}{3} \frac{N}{V} \left(\frac{1}{2}m\bar{v^2}\right) = \frac{2}{3} \frac{N}{V} (K.E)_{avg}$.
- Absolute temperature of a gas is measure of its average translational K.E of all gas molecules.
- $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$.
- RMS speed: $v_{rms} = \sqrt{\bar{v^2}} = \sqrt{\frac{3KT}{m}}$.
- Average speed of oxygen molecules in air at STP is $461~m s^{-1}$, for nitrogen it is $493~m s^{-1}$.
Specific Heats
- Amount of heat required to raise temperature of substance through 1 K.
- $Q = Cm\Delta T$.
- Specific heat is amount of heat required to raise temperature of unit mass through unit temperature.
- Molar specific heat of diatomic gas is greater than that of monatomic gas.
Introduction to Thermodynamics
- Study of relationship between heat and other forms of energy.
- Thermodynamic states describe state of a system.
- Any collection of matter having distinct boundaries is called a system.
- Boyle's Law: $PV = \text{constant}$ (Isothermal process).
- Charles's Law: $\frac{V}{T} = \text{constant}$ (Isobaric process).
- Total translational K.E, rotational K.E, vibrational K.E, and P.E due to intermolecular forces is called internal energy.
- Internal energy of an ideal gas system is translational K.E of its molecules.
- Increase in temperature indicates increase in internal energy.
- Thermodynamic work at constant pressure is $W = P\Delta V$. If pressure is not constant, $W = \sum P\Delta V$.
Laws of Thermodynamics
-
First Law of Thermodynamics
- Energy can be transformed from one form to another, but total amount of energy remains constant.
- $\Delta Q = \Delta U + \Delta W$.
- $\Delta Q$: heat added to system (+ve) or removed from system (-ve).
- $\Delta U$: change in internal energy (+ve for increase, -ve for decrease).
- $\Delta W$: work done by system (+ve for expansion), work done on system (-ve for compression).
- For a cyclic process, $\Delta U = 0 \implies \Delta Q = \Delta W$.
-
Second Law of Thermodynamics
- Kelvin Statement: It is impossible to construct a heat engine which converts all heat energy absorbed from source without having a sink.
- Clausius' Statement: Heat cannot flow spontaneously from a colder body to a hotter body without external work.
- Refrigerator: Heat engine operating in reverse, transfers heat from cold to hot region.
Applications of First Law of Thermodynamics (Thermodynamic Processes)
- Isothermal Process: Temperature remains constant. $\Delta Q = \Delta W$, $\Delta U = 0$. (Process should be very slow). Example: Isothermal expansion of ideal gas.
- Isochoric (Isovolumetric) Process: Volume remains constant. $\Delta W = 0$, $\Delta Q = \Delta U$. (Heat supplied at constant volume). Example: Melting of ice, boiling of water.
- Isobaric Process: Pressure remains constant. $\Delta P = 0$, $\Delta Q = \Delta U + P\Delta V$. (Heat supplied at constant pressure). Example: Burst of air tube.
- Adiabatic Process: No heat enters or leaves the system. $\Delta Q = 0$, $\Delta U = -\Delta W$. (Process should be very rapid and system thermally insulated). Example: Propagation of sound in air, explosion in gases.
- Isentropic Process: Reversible adiabatic process (entropy remains constant).
-
Work Done by Thermodynamic System
- Energy transferred by a system to other owing to a force that acts between them.
- Work done by a system is positive if volume increases (expansion).
- Work done on a system is negative if volume decreases (compression).
- Work done by indicator-diagram (P-V diagram) is area under the curve. Positive for clockwise direction (expansion), negative for anti-clockwise (compression).
-
Comparison of Different Thermo Dynamical Processes
Sr. No. Property Isothermal Adiabatic Isochoric Isobaric 1. Condition T=constant Q=constant V=constant P=constant 2. Form of first Law $\Delta Q = \Delta W$ $\Delta U = -\Delta W$ $\Delta Q = \Delta U$ $\Delta Q = \Delta U + P\Delta V$ 3. P.V Diagram 4. Equation of state $PV=\text{constant}$ $PV^\gamma=\text{constant}$ $\frac{P}{T}=\text{constant}$ $\frac{V}{T}=\text{constant}$ 5. Specific Heat $c=\infty$ $c=0$ $c=C_V$ $c=C_P$ 6. Slope of P.V curve $\frac{\Delta P}{\Delta V} = -\frac{P}{V}$ $\frac{\Delta P}{\Delta V} = -\gamma\frac{P}{V}$ $\frac{\Delta P}{\Delta V} = \infty$ $\frac{\Delta P}{\Delta V} = 0$ 7. Elasticity $E=P$ $E=\gamma P$ $E=\infty$ $E=0$ 8. Operating condition Process should be completed very slowly Process is to be completed rapidly and the system should be surrounded by thermally insulated medium To supply heat at constant volume. Melting of ice, Boiling of water 9. Example Isothermal expansion of ideal gas Propagation of sound in air, explosion in gases Atmospheric changes Boiling of water - $C_p$ is greater than $C_v$.
- $\Delta Q_v = n C_v \Delta T$ (Heat supplied at constant volume).
- $\Delta Q_p = n C_p \Delta T$ (Heat supplied at constant pressure).
- $C_p - C_v = R$.
- $\gamma = \frac{C_p}{C_v}$.
Reversible and Irreversible Processes
- Reversible Process: Sequence of processes carried out in such a manner that the values of thermodynamic variables are retrieved at end of processes. Example: Liquefaction, evaporation, compression performed slowly.
- Irreversible Process: All changes that occur suddenly or involve friction or dissipation of energy through conduction, convection or radiation.
Heat Engine
- Thermodynamic device that converts heat energy into mechanical energy.
- No perfect heat engine exists.
- Always operates in a cycle.
- Cycle means set of changes which bring system to its initial state.
- Area under PV graph gives work done by engine.
-
Carnot Heat Engine (Ideal Engine)
- Proposed by Sadi Carnot in 1840.
- Has maximum efficiency, but not 100%.
- Efficiency: $\eta_c = \left(1-\frac{T_L}{T_H}\right) \times 100$. ($T_L$: temperature of cold reservoir/sink, $T_H$: temperature of hot reservoir/source).
- Carnot cycle consists of: (i) Isothermal expansion, (ii) Adiabatic expansion, (iii) Isothermal compression, (iv) Adiabatic compression.
- Efficiency depends on temperature difference between source and sink.
- Independent of nature of working substance.
- 100% efficiency only when $T_L = 0~K$ (absolute zero), which is practically impossible.
-
Classification of Heat Engine
- Internal Combustion Engine (e.g., Petrol Engine, Diesel Engine).
- External Combustion Engine.
Petrol Engine (Four-stroke cycle principle):
- Cylinder, Piston, Crank shaft, Connecting rod.
- Four successive processes:
- Intake Stroke: Piston moves down, intake valve open, fuel enters.
- Compression Stroke: Piston moves up, both valves closed, fuel compressed.
- Power Stroke (Ignition): Piston moves down, both valves closed, burnt gases expand.
- Exhaust Stroke: Piston moves up, exhaust valve open, burnt gases expelled.
- Efficiency of petrol engine is about 25% to 30%.
- Diesel engine has no spark plug. Efficiency is about 35% to 40%.
Entropy
- Degree of disorderliness is called statistical entropy.
- Unavailability of heat energy is called thermo entropy.
- Law of increase of entropy: Entropy of a thermodynamic system either remains constant (during reversible process) or it increases (during irreversible process).
- Change in entropy: $\Delta S = \frac{\Delta Q}{T}$.
- Unit: $J~K^{-1}$.
- Entropy may remain constant for a reversible process.
- Entropy increases for all irreversible processes.
- Environmental crisis is an entropy or disorder crisis.
| Entropy | Definition |
|---|---|
| Entropy | A state variable whose change is defined for a reversible process at $T$ where $Q$ is the heat absorbed. |
| Entropy | A measure of the amount of energy which is unavailable to do work. |
| Entropy | A measure of the disorder of a system. |
| Entropy | A measure of the multiplicity of a system. |