Page 88 - DJJ20063- Thermodynamics 1

DJJ20063- Thermodynamics 1

The expansion work is given by

2
W =  pdV
1

2 c
=  dV (since pV = C, a constant)
1 V
2 dV
= c 
1 V
2 dV
= p V 
1 1 V
1
V  larger vol ume 
p
= V 1 ln 2  
1
V 1 smaller vo lume 
V
= mRT 1 ln 2 (since p1V1 = mRT1)
V 1

p V p
= mRT ln 1 (since 2 = 1 ) (3.4)
1
p 2 V 1 p 2

Note that during expansion, the volume increases and the pressure decreases. On the p

– V diagram, the shaded area under the process line represents the amount of work

transfer.

Since this is an expansion process (i.e. increasing volume), the work is done by the system.

In other words the system produces work output and this is shown by the direction of the

arrow representing W.

Heat transfer:

Energy balance to this case is applied:

U1 + Q = U2 + W

For a perfect gas

U1 = mcvT1 and U2 = mcvT2

As the temperature is constant

U1 = U2

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