Page 11 - Hsslive-Plus-One-Physics-Class-Notes-Part-III (1)

Heat, Thermodynamics & Kinetic Theory {10} Vinodkumar M, St. Aloysius H.S.S, Elthuruth, Thrissur.

V 2 
Or work done, W = 2.303 R T log 10  
 V 1 
But P V = P V .
1 1 2 2
V 2 P 1
Or 
V 1 P 2

P 1 
 W = 2.303 R T log 10  P 
 2 

Work done in an adiabatic process
Let an ideal gas undergoes adiabatic charge from (P , V , T ) to (P , V , T ).
1 1 1 2 2 2
The equation for adiabatic charge is PV  = constant = k.

 
ie; P V  P V  k ........... (a).
1 1 2 2
The work done
V
2
W   P dV
V 1
V 2 dV
W  k  V  (since P  k  )
1 V V

V   1 V 2 k  1 1  1  k k  1  VP 2 2  P 1 V 1  
W = k    1   1     1   1     1   1 
  1 1   V V  1   V V  1    V V 


V 1 2 1 2 1 2 1
from equation (a)
1
W = P V  P V 1
2
1
2
1 
1 R
W = P V  P V 1 = T ( 2  T 1 )
2
1
2
1  1  
Substituting ideal gas equation.
1 R
W = P V 1  P V 2 or W  T  T 2
1
1
2
  1   1
Workdone in isochoric process.
Here V = constant, Small workdone, dW = PdV. Here dV = 0 , therefore,W = 0.
Work done in an isobaric process
Here P = constant. dW = PdV. The total workdone to change the volume from V to V , W = P (V - V )
1 2 2 1

Q4. One mole of a gas at 27 C expands adiabatically until its volume is doubled. Calculate the workdone?
o
[1519 J]

Cyclic process
In cyclic process, the system returns to its initial state such that
charge internal energy is zero. The P - V diagram for cyclic process
will be closed loop and area of this loop gives work done or heat
absorbed by system.