physics-class-11-unit-12-chapter-03-heat-engine-and-refrigerators-l-7-9-lydxzor5kcy

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Recap </primary>
<hr>
<main>

- Work done in different thermodynamic Processes

- Quasi-static

- Ideal Gas: $P V=n R T$

- Isothermal process: Temperature remains fixed. Internal energy (function of) does not change Pressure and Volume change

- $P_1, V_1, T \Rightarrow P_2, V_2, T $

- $P_1 V_I=C_I \rightarrow$ Isothermal process

</div>

<div style='float: right; width:0%;'>
	
![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-12-chapter-03-heat-engine-and-refrigerators-l-7_9-lydxzor5kcy-1.jpg)

</main>
<hr>
<footer style = "font-size: 18px"> $\rightarrow$ Heat Engine and Refrigerators $\rightarrow$ <span style = "color:blue"> Recap </span> $\rightarrow$ Isothermal process $\rightarrow$ First law of Thermodynamics </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Isothermal process </primary>
<hr>
<main>

- $W=\int_{V_1}^{V_2} P d V=n R T \ln \frac{V_2}{V_1}$

- Expansion $V_2>V_1 \quad$ : work done in positive: System absorbs heat and coverts to work.

- Contraction $V_1>V_2$ : work done is negative (done on the system): work is done on the system and it releases heat.

</main>
<hr>
<footer style = "font-size: 18px">Heat Engine and Refrigerators $\rightarrow$ Recap $\rightarrow$ <span style = "color:blue"> Isothermal process </span> $\rightarrow$ First law of Thermodynamics $\rightarrow$ Isothermal process Alternative method </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Isothermal process Alternative method </primary>
<hr>
<main>

- $P V=n R T, \quad V=\frac{n R T}{P} $

- $d V=-\frac{n R T}{p^2} d P$

- $W =\int_{V_1}^{V_2} PdV ; $

- $=-n R T \int_{P_1}^{P_2} \frac{P}{P^2}$

- $=-n R T \ln \frac{P_2}{P_1}$

- $P_2 V_2=P_1 V_1 \Rightarrow n R T = C_I$

- $ W =-n R T \ln \frac{V_1}{V_2} = n R T \ln \frac{V_2}{V_1}$

</main>
<hr>
<footer style = "font-size: 18px">Isothermal process $\rightarrow$ First law of Thermodynamics $\rightarrow$ <span style = "color:blue"> Isothermal process Alternative method </span> $\rightarrow$ Isochoric Process $\rightarrow$ Isobaric Process </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Isochoric Process </primary>
<hr>
<main>

- Isochoric Process: Volume is kept fixed, <span style="color:green">But temperature and pressure change, Internal energy changes.</span>

- $P_1, V, T_1 \Rightarrow P_2, V, T_2 $

- No work done $\int P d V=0$

- Heat absorbed or released = Change in internal energy

- Heat absorbed $\rightarrow$ Temperature increases $\rightarrow$ Pressure increases, Internal energy increases.

- Heat released $\rightarrow$ Internal energy decreases

- $\delta Q = d U$ as $ W = 0$.

- $P \propto T$ if $V$ is constant.

</main>
<hr>
<footer style = "font-size: 18px">First law of Thermodynamics $\rightarrow$ Isothermal process Alternative method $\rightarrow$ <span style = "color:blue"> Isochoric Process </span> $\rightarrow$ Isobaric Process $\rightarrow$ Adiabatic Process </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Isobaric Process </primary>
<hr>
<main>

- Pressure is constant: <span style="color:green">Volume and temperature change</span>

- $P, V_1, T_1 \Rightarrow P, V_2, T_2$

- <span style="color:green">Internal energy change</span>: $W=P\left(V_2-V_1\right)=n R\left(T_2-T_1\right)$

- <span style="color:green">Exapansion</span> $V_2>V_1 \Rightarrow T_2>T_1$ : Work done is positive, Change in internal energy is positive. System absorbs heat

- $\delta Q=d V+\delta W $

- <span style="color:green">Contraction</span> $V_1>V_2 \Rightarrow T_1>T_2:$ Work done is negative, Change in internal energy is negative. System releases heat

- $V \propto T $, $P V=n R T$

</main>
<hr>
<footer style = "font-size: 18px">Isothermal process Alternative method $\rightarrow$ Isochoric Process $\rightarrow$ <span style = "color:blue"> Isobaric Process </span> $\rightarrow$ Adiabatic Process $\rightarrow$ Curves </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Adiabatic Process </primary>
<hr>
<main>

- Adiabatic Process: No heat exchange: Pressure, temperature and volume change $\delta Q = 0$

- $P_1, V_1, T_1 \Rightarrow P_2, V_2, T_2$

- $ C_P-C_V=R$

- $P V^\gamma$= constant

- $\gamma=\frac{C_P}{C_V} ; \gamma>1$

- Isothermal: $P_I V_I=C_I$

- Adiabatic: $P_A V_A^\gamma=C_A$

- $P_I=\frac{C_I}{V_I},\left(\frac{\partial P_I}{\partial V_I}\right)=-\left.\frac{C_I}{V_I^2}\right|_{{V_0},{P_0}}$

</div>
	
<div style='float: right; width:0%;'>
		
![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-12-chapter-03-heat-engine-and-refrigerators-l-7_9-lydxzor5kcy-8.jpg)
		
![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-12-chapter-03-heat-engine-and-refrigerators-l-7_9-lydxzor5kcy-9.jpg)

</main>
<hr>
<footer style = "font-size: 18px">Isochoric Process $\rightarrow$ Isobaric Process $\rightarrow$ <span style = "color:blue"> Adiabatic Process </span> $\rightarrow$ Curves $\rightarrow$ Curves </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Curves </primary>
<hr>
<main>

- Isothermal: $P_I V_I=C_I$

- $P_I=\frac{C_I}{V_I},\left(\frac{\partial P_I}{\partial V_I}\right)=-\left.\frac{C_I}{V_I^2}\right|_{{V_0},{P_0}}$

- $ = - \left.\frac{P_I V_I}{V_I^2}\right|_{V_0, P_0}$

- $= - \left.\frac{P_I V_I}{V_I^2}\right|_{P_0, V_0} =-\frac{P_0}{V_0}$

- Adiabatic: $P_A V_A^\gamma=C_A$

- $\left(\frac{\partial P_A}{\partial V_A}\right)_{P_0, V_0}=$

- $-\frac{\gamma C_A}{V_A^{\gamma+1}}|_{P_0, V_0}$

</main>
<hr>
<footer style = "font-size: 18px">Isobaric Process $\rightarrow$ Adiabatic Process $\rightarrow$ <span style = "color:blue"> Curves </span> $\rightarrow$ Curves $\rightarrow$ Curves </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Curves </primary>
<hr>
<main>

- Expansion Process:  $V_0 \rightarrow V_2 $

- Contraction process:  $V_0 \rightarrow V_1$

- Work done in the Isothermal process is more.

- Contraction process: $\longrightarrow$ Adiabatic work done is more.

</div>

</main>
<hr>
<footer style = "font-size: 18px">Curves $\rightarrow$ Curves $\rightarrow$ <span style = "color:blue"> Curves </span> $\rightarrow$ Work done $\rightarrow$ Quasi-static </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Work done </primary>
<hr>
<main>

- $W=\frac{1}{1-\gamma}\left[P_2 V_2-P_1 V_1\right]=n R \frac{\left(T_1-T_2\right)}{\gamma-1} ; \gamma>1$

- $T_1>T_2$ Internal energy decreases: Work done is positive

- $T_2>T_1$ Internal energy increases: Work done is negative

- $P_1 V_1^\gamma=P_2 V_2^\gamma=C_A \Rightarrow P_1=\frac{C_A}{V_1^\gamma} ; P_2=\frac{C_A}{V_2^\gamma}$

- $W=\frac{1}{1-\gamma}\left[P_2 V_2-P_1 V_1\right]=\frac{C_A}{1-\gamma}\left(\frac{1}{V_2^{\gamma-1}}-\frac{1}{V_1^{\gamma-1}}\right)$

</div>

![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-12-chapter-03-heat-engine-and-refrigerators-l-7_9-lydxzor5kcy-13.jpg)

</main>
<hr>
<footer style = "font-size: 18px">Curves $\rightarrow$ Curves $\rightarrow$ <span style = "color:blue"> Work done </span> $\rightarrow$ Quasi-static $\rightarrow$ Reversible Heat Engines </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Quasi-static </primary>
<hr>
<main>

- Quasi-static and non-dissipative: No friction or viscosity

- Forward process $\rightarrow P_1,V_1,T_1 \Rightarrow P_2,V_2,T_2$

- Backward process $\rightarrow P_2,V_2,T_2 \Rightarrow P_1,V_1,T_1$

| Forward | Backward |
| -------- | -------- |
| $\Delta Q$    | -$\Delta Q$     |
| $\Delta W$    | -$\Delta W$     |
| $\Delta U$    | -$\Delta U$     |

</main>
<hr>
<footer style = "font-size: 18px">Curves $\rightarrow$ Work done $\rightarrow$ <span style = "color:blue"> Quasi-static </span> $\rightarrow$ Reversible Heat Engines $\rightarrow$ Efficiency of an Engine </footer>

### <Success style="font-size:25px"> Heat Engine And Refrigerators L-7 </Success>
### <primary style="font-size:24px"> Reversible Heat Engines </primary>
<hr>
<main>

- a. Working substance: steam in steam engines: Ideal Gas.

- b. The working goes in a closed cycle:multiple thermodynamic processes.

- $(P, T, V)\longrightarrow(P, V, T)$

- c. Works in a closed loop between two heat reservoirs:

- Hot reservoir $T_1$ and cold reservoir  $T_2$ ,  $T_1>T_2$

- In a closed loop:

- Heat absorbed from the hot reservoir: $Q_1$

- Heat released to thecold reservoir: $Q_2$

- Work done by the system $ W=Q_1-Q_2$

</main>
<hr>
<footer style = "font-size: 18px">Work done $\rightarrow$ Quasi-static $\rightarrow$ <span style = "color:blue"> Reversible Heat Engines </span> $\rightarrow$ Efficiency of an Engine $\rightarrow$ Refrigerator </footer>