Page 1 Important Formulae 1. Thermodynamics (i) Molar heat capacity C = heat required to raise the temperature of 1 mole of any substance by 1 °C or 1 K. Q nT ? ? Q = nC ?T Molar heat capacity of solids and liquids is almost constant. In case of gases C is process dependent. It varies from 0 to ?. In isothermal process, C = ? as ?T = 0 In adiabatic process, C = 0 as Q = 0 C p (molar heat capacity of isobaric process) and C v (molar heat capacity of isochoric process) are commonly used. In a general process pV x = constant, molar heat capacity is given by, RR C 1 1 x ?? ? ? ? (ii) First law of thermodynamics It is a law of conservation of energy given by, Q = ?U + W (iii) Detailed discussion of three terms of first law of thermodynamics (a) Work done Following methods are generally used to find the work done, Method 1 i i V V W pdV ? ? (because dW = pdV) Here, p should be either constant or function of V. If p is constant. It means process is isobaric, W = p(V f â€“ V i ) = p ?V Method 2 Work done can also be obtained by area under p-V diagram with projection on V-axis. W = + ve as volume is increasing W = - ve as volume is decreasing Page 2 Important Formulae 1. Thermodynamics (i) Molar heat capacity C = heat required to raise the temperature of 1 mole of any substance by 1 °C or 1 K. Q nT ? ? Q = nC ?T Molar heat capacity of solids and liquids is almost constant. In case of gases C is process dependent. It varies from 0 to ?. In isothermal process, C = ? as ?T = 0 In adiabatic process, C = 0 as Q = 0 C p (molar heat capacity of isobaric process) and C v (molar heat capacity of isochoric process) are commonly used. In a general process pV x = constant, molar heat capacity is given by, RR C 1 1 x ?? ? ? ? (ii) First law of thermodynamics It is a law of conservation of energy given by, Q = ?U + W (iii) Detailed discussion of three terms of first law of thermodynamics (a) Work done Following methods are generally used to find the work done, Method 1 i i V V W pdV ? ? (because dW = pdV) Here, p should be either constant or function of V. If p is constant. It means process is isobaric, W = p(V f â€“ V i ) = p ?V Method 2 Work done can also be obtained by area under p-V diagram with projection on V-axis. W = + ve as volume is increasing W = - ve as volume is decreasing W = 0 as volume is constant W = +ve as cyclic process is clockwise with p on y-axis. (b) Change in internal energy ?U ?U = nC V ?T for all processes. For this C V (or nature of gas), n and ?T should be known. If either of the three terms is not known, we can calculate ?U by, ?U = Q - W (c) Heat exchange Q Q = nC ?T. For this n, ?T and molar heat capacity C should be known. C is a process dependent. So, if either of the three terms (n, ?T or C) is not known, we can calculate Q by, 0 = ?U + W (iv) dp p x dV V ?? in process pV x = constant or slope of p-V graph = p x V ? In isobaric process x = 0, therefore slope = 0 In isothermal process x = 1, therefore slope = p V ? In adiabatic process x = ?, therefore slope = p V ??Read More

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