Heat, Internal Energy and Work, First Law of Thermodynamics

  • Heat is the energy that is transferred between a system and its surrounding and heat is a path dependent quantity.
  • Internal energy of a system is the energy possessed by the system due to molecular motion and molecular configuration.
  • The energy due to molecular motion is internal KE UK and heat due to molecular configuration U = Uk + Up
  • Change in internal energy (du) is path independent and depends only on the initial and final state du = Uf − Ui
  • The amount of external work done by a system it expands or contracts \tt \int dw=\int_{V_1}^{V_2}P\ dv work is path dependent.
  • In a cyclic process work done is equal to the area under the cyclic. In this case W is +ve if the cycle is clockwise and W is −ve if the cycle is anticlock wise.
  • According to the first law of thermodynamics heat given to a system (dQ) is equal to the sum of increase in its internal energy (du) and work done (dw) by the system dQ = du + dw
  • dQ is +ve when heat is supplied and −ve when heat rejected. du is +ve when temperature increases and −ve when temperature decreases.
  • dw is +ve when work done by system.
    dw is −ve when work done on system.
  • First law of thermodynamics is a consequence of law of conservation of energy.

View the Topic in this video From 7:00 To 57:40

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1. The first law of thermodynamics is the general law of conservation of energy applied to any system in which energy transfer from or to the surroundings (through heat and work) is taken into account. It states that
ΔQ = ΔU + ΔW

2. The specific heat capacity of a substance is defined by
s = \frac{1}{m} \frac{\Delta Q}{\Delta T}

3. For gases when heat is absorbed and temperature changes ⇒ ΔQ = μCΔT
At constant pressure (ΔQ)P = μCPΔT
At constant volume (ΔQ)V = μCVΔT

4. Internal energy of an ideal gas is totally kinetic and is given by U = U_{k} = \frac{3}{2} \mu RT and change in internal energy \Delta U = \frac{3}{2} \mu R \Delta T

5. Isothermal Process : In this process, temperature of the system is kept constant during the changing of state.
As, Q = nC_{iso}dT \Rightarrow C_{iso} = \frac{Q}{ndT} = \infty

6. Adiabatic process: In this process, no exchange of heat takes place between the system and surroundings, i.e., dQ = 0 or Q = 0
Work done, W = \frac{nR(T_{1} - T_{2})}{\gamma - 1} = \frac{p_{1}V_{1} - p_{2}V_{2}}{\gamma - 1}

7. Isobaric process : This is the process in which pressure is kept constant.
(i) Molar heat capacity of the process is Cp and dQ = nCpdT and dU = nCvdT.
(ii) From the first law of thermodynamics,
dQ = dU + dW
and dW = pdV = nRdT ⇒ dQ = dU + nRdt
Process equation is \frac{V}{T} = constant.

8. Cyclic process: In a cyclic process, the system returns to its initial state.
Efficiency of the cycle, \tt \eta = \frac{work \ done}{Heat \ Supplied}