Thermodynamics system

  1. \toIt is an assembly of an extremely large number of particles (atoms or molecules)\\having a certain pressure, volume and temperature.\\\toIt is of two types:\\1)Isolated System: (no heat can enter or leave out the system)\\2)Closed system: (There can be heat exchange between the system and surrounding)\\

  2. \textbf{Thermal Equilibrium:}\\A thermodynamics system is in thermal equilibrium if the temperature of all parts of it is same.

Zeroth law of Thermodynamics

When two bodies A and B are in thermal equilibrium with third body C then the body A and B\\also must be in thermal equilibrium with each other.

Work Done

  1. Points:\\

    \toWork is said done when volume of gas changes.\\

    \toWork done is positive if expansion takes place and is negative if compression takes place.\\

    Work (W) = PdV\\

    \toArea under PV curve between volume axis is equal to work done.\\

    \toFor a closed cycle, area of closed loop gives work done.\\

    \toWhen P remains constant throughout the expansion, the work done by the gas is\\


  2. \textbf{Internal Energy of a Gas}\\The sum of energy due to molecular motion (KE) and due to molecular configuration (PE)\\is called internal energy of gas.\\:. Internal energy (U) = PE + KE\\For ideal gas intermolecular force of attraction is neglected so PE=0,\\so internal energy of ideal gas is KE which is only the function of temperature.

First law of thermodynamics

  1. When heat energy is given to a system then some part of heat energy supplied is used to\\change the internal energy of system and rest of energy is used to do external work.\\∆Q=∆U+∆W\\

  2. \textbf{Note:}\\For cyclic process, the change in internal energy of the system is zero because the system is\\brought back to the initial condition. Therefore, dU=0 and from the first law of thermodynamics,\\dQ= du + PdV =0+dW= dW\\

  3. \textbf{Molar Heat Capacities:}\\1)Molar heat capacity at constant pressure (C_p)\\\toHeat required to rise the temperature of one mole of gas through 1 degree C at constant pressure.\\Its unit is J/(molK)\\\toHeat required (dQ)=nC_pdT\\2)Molar heat capacity at constant volume(C_v):\\\toHeat required to rise the temperature of mole of gas through 1 degree C at constant volume.\\Its unit is J/(molK)\\\toHeat required (dU) = nC_vdT\\

  4. \textbf{Mayer`s Formula:}\\\to C_p-C_v=R

Specific heat capacities

  1. (c_p)\\\toHeat required to rise the temperature of unit mass of gas through 1 degree C temperature\\at constant pressure. \toHeat required (dQ)=mc_pdT\\\to C_p=Mc_p \\

  2. \textbf{Specific heat capacity at constant volume :}(c_v)\\\toHeat required to rise the temperature of unit mass gas through 1 degree C temperature\\at constant volume. \toIts unit is J/(kg K)\\\toHeat required (du)=mc_vdT\\\to C_v=Mc_v \\

  3. \textbf{Note:}\\\toHeat required to rise certain temperature at constant pressure is always greater than heat\\required to rise same temperature at constant volume. So gas has two types of heat capacities\\\to i.e. C_p>C_v \\\toBecause in constant pressure, internal energy and work done both is done.

Thermodynamical process

  1. \toVolume remains constant\\\toWork done (dw)=0\\\to Heat supplied = change in internal energy: dQ=dU\\\tonCvdT=dU\\

  2. \textbf{ Isobaric Process:}\\\toPressure remains constant\\\todQ=CvdT+ PdV\\

  3. \textbf{Isothermal Process:}\\\toTemperature remains constant. i.e. dT=0\\\toFor this process cylinder with conducting wall is used and ideal gas filled inside is allowed to\\expand or is compressed very slowly.\\\toEg: Melting process and boiling process\\\toSpecific heat capacity during isothermal process is infinity\\\toChange in internal energy(du)= 0\\\toGas Equation: P_1 V_1=P_2 V_2 \\\toSlope of curve (dP/dV)=-P/V\\\toWork Done (w) =nRT ln(V_2/V_1)\\=P_1 V_1 ln(V_2/V_1)=P_1 V_1 ln(P_1/P_2)\\

  4. \textbf{Adiabatic Process: }\\\toThe process in which exchange of heat energy is zero i.e. dQ=0\\\toSo, dW=-dU i.e. work is done by gas on the expense of internal energy so cooling is observed after\\adiabatic expansion\\\toFast process in which wall of cylinder is perfectly insulator\\\toSpecific Heat capacity of gas is 0.\\\toEg: Propagation of sound wave, sudden bursting of tire, the compression stroke in an internal\\combustion engine.\\\toSlope of curve (dP/dV)=-γP/V\\\toGas equation is\\P_1 V_1^γ=P_2 V_2^γ \\T_1 V_1^{γ-1}=T_2 V_2^{γ-1} \\T_1^γ/P_1^{γ-1} =T_2^γ/P_2^{γ-1}\\