Physics > First Law of Thermodynamics > 4.0 Different thermodynamic processes
First Law of Thermodynamics
1.0 Introduction
2.0 Three important terms in first law of thermodynamics.
3.0 First law of thermodynamics
4.0 Different thermodynamic processes
4.1 Isobaric Process:
4.2 Isochoric process
4.3 Isothermal process
4.5 Adiabatic process
4.6 Polytropic process
5.0 Graphs
6.0 Efficiency of cyclic process
7.0 Heat engine
8.0 Refrigerator
4.1 Isobaric Process:
4.2 Isochoric process
4.3 Isothermal process
4.5 Adiabatic process
4.6 Polytropic process
Isobaric process is a process in which pressure remains constant
$$ \Rightarrow dP = 0$$ We can show isobaric process in $P - V$ graph as
In an isobharic process $P$ =constant or $\Delta P$=0
$V \propto T$ or $\frac{V}{T}$=constant
$$W = P\Delta V = P({V_f} - {V_i})$$$$ = nR({T_f} - {T_i}) = nR\Delta T$$$$\Delta U = n{C_V}({T_f} - {T_i}) = n{C_V}\Delta T$$$$Q = W + \Delta U = nR\Delta T + n{C_V}\Delta T$$$$ = n\Delta T({C_V} + R)$$$$ = n{C_P}\Delta T$$
In an isobaric process
$$Q:\Delta U:W = {C_P}:{C_V}:R$$
Question 11. Find the ratio of $\frac{{\Delta Q}}{{\Delta U}}$ and $\frac{{\Delta Q}}{{\Delta W}}$ in an isobaric process. The ratio of molar heat capacities $\frac{{{C_P}}}{{{C_V}}} = \gamma $.
Solution: In an isobaric process $P$ = constant. Therefore, $C = {C_P}$. $$\frac{{\Delta Q}}{{\Delta U}} = \frac{{n{C_P}\Delta T}}{{n{C_V}\Delta T}} = \frac{{{C_P}}}{{{C_V}}} = \gamma $$ $$\begin{equation} \begin{aligned} \frac{{\Delta Q}}{{\Delta W}} = \frac{{\Delta Q}}{{\Delta Q - \Delta U}} \\ = \frac{{n{C_P}\Delta T}}{{n{C_P}\Delta T - n{C_V}\Delta T}} \\ = \frac{{{C_P}}}{{{C_P} - {C_V}}} = \frac{{\frac{{{C_P}}}{{{C_V}}}}}{{\frac{{{C_P}}}{{{C_V}}} - 1}} \\ = \frac{\gamma }{{\gamma - 1}} \\\end{aligned} \end{equation} $$
