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
4.2 Isochoric process
4.2 Isochoric process
4.3 Isothermal process
4.5 Adiabatic process
4.6 Polytropic process
Isochoric process is a process in which volume remains constant
In an isochoric process,
$V$ =constant or $\Delta V$
$$P \propto T$$ $$ \Rightarrow \frac{P}{T}$$
As $V$ is constant, $$dV = 0$$ We can show isochoric process in $P - V$ graph as
Work done by gas=$0$ [since volume is constant]
$$Q = \Delta U = n{C_V}\Delta T$$
All heat supplied to the gas converts into internal energy of gas.
We can show isochoric process in $P-T$ graph Question 12. What is the heat input needed to raise the temperature of $2$ moles of helium gas from ${0^0}\;to\,{100^0}C$
(a) at constant volume
(b) at constant pressure
(c) What is the work done by the gas in part (b)?
Give your answer in terms of $R$.
Solution: Helium is monoatomic gas, therefore, $${C_V} = \frac{{3R}}{2}\;and\;{C_P} = \frac{{5R}}{2}$$(a) At constant volume, $$\begin{equation} \begin{aligned} Q = n{C_V}\Delta T \\ = \left( 2 \right)\left( {\frac{{3R}}{2}} \right)\left( {100} \right) \\ = 300R \\\end{aligned} \end{equation} $$(b) At constant pressure,$$\begin{equation} \begin{aligned} Q = n{C_P}\Delta T \\ = \left( 2 \right)\left( {\frac{{5R}}{2}} \right)\left( {100} \right) \\ = 500R \\\end{aligned} \end{equation} $$(c) At constant pressure,$$\begin{equation} \begin{aligned} W = Q - \Delta U \\ = n{C_P}\Delta T - n{C_V}\Delta T \\ = nR\Delta T = \left( 2 \right)\left( R \right)\left( {100} \right) \\ = 200R \\\end{aligned} \end{equation} $$
