Thermodynamics Concept Page - 8

Example

Expanding liquid inside an expanding solid

A vessel of volume 1liter$1liter$ is filled with a liquid whose coefficient of volume expansion is 20$20$ times as that of the vessel. At all temperatures if volume of air above the liquid is constant the volume of that empty space is:γlVl=γcVc${\gamma }_l{V}_l={\gamma }_c{V}_c$ where 
γl${\gamma }_l$- volume expansion coefficient of the liquid
γc${\gamma }_c$ - volume expansion coefficient of the container
Vl$V_l$ - volume of the liquid
Vc$V_c$ - volume of the container
Since the volume of the empty space above the liquid remains constant, ΔVc=ΔVl$\mathrm{\Delta }{V}_c=\mathrm{\Delta }{V}_l$
∴20γcVl=γcVc$\therefore 20{\gamma }_c{V}_l={\gamma }_c{V}_c$
⇒VcVl=20$\Rightarrow {\displaystyle \frac{V_c}{V_l}}=20$
Vc−VlVc=20−120=1920${\displaystyle \frac{V_c-V_l}{V_c}}={\displaystyle \frac{20-1}{20}}={\displaystyle \frac{19}{20}}$
Vc−Vl=1920×1litre=950ml=950cc$V_c-V_l={\displaystyle \frac{19}{20}}\times 1litre=950ml=950cc$

Definition

Heat capacity

Heat capacity (c′$c^{\prime }$) of a body is defined as the amount of heat energy required to raise its temperature by 1 K$1K$.
c′=QΔt$c^{\prime }={\displaystyle \frac{Q}{\mathrm{\Delta }t}}$

Definition

SI unit of heat capacity

The SI unit of heat capacity is JK−1$J{K}^{-1}$. 

Example

Specific heat capacity of common substances

Substance	Specific heat capacity (J kg−1K−1$Jk{g}^{-1}{K}^{-1}$)	Specific heat capacity (cal g−1 oC−1$cal{g}^{-1o}{C}^{-1}$)
Mercury	130	0.031
Copper	399	0.095
Glass(flint)	504	0.12
Aluminium	882	0.21
Ice	2100	0.50
Sea water	3900	0.95
water	4180	1.0

Definition

Quasi-static process

A quasi-static process is an idealised hypothetical process in which all changes take place infinitely slowly. An example of this is quasi-static compression, where the volume of a system changes at a rate slow enough to allow the pressure to remain uniform and constant throughout the system.

Definition

Isobaric Process

An isobaric process is one in which the pressure is constant. The simplest example is the heating of water in an open vessel. 

Formula

Work done in an isobaric process

W=P(V2−V1)=nR(T2−T1)$W=P(V_2-V_1)=nR(T_2-T_1)$
where the subscript 1 and 2 represents initial and final states respectively

Diagram

PV diagram for an isobaric process

Definition

Work done in an isobaric process by PV curve

The area under the PV curve is a rectangle of length V2−V1$V_2-V_1$ and breadth P1=P2$P_1=P_2$
So work done = area under the curve = P1(V2−V1)$P_1(V_2-V_1)$

Diagram

VT, PT graphs for an isobaric process

BookMarks

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