can you help solve this??

[bantamm]

a gas expands adaibatically behind a piston according to the law p=2000V^-14

find the mean effective pressure p(mean value) for the expansion from a volume V from 0.5m3 to 2m3

then determine the work done (W)
note: W=pmean x deltaV



help!!!!!!!!!!!

 

[Quibbler]

Phew that's a pretty non-ideal gas.

I think you need to integrate from V(initial) to V(final)

w=∫P dV=∫2000V^-14 dV

 

[steve10]

Honestly, I am not so confident about this. Here is what I got.

Set
V1=0.5
V2=2

Then deltaV=V2-V1=1.5

Now,
p(mean value)=Integrate[V*p, {V,V1,V2}]=Integrate[2000V^-13, {V,V1,V2}]
=(2000/12)*(V1^-12 - V2^-12)
=(500/3)*(0.5^-12 - 2^-12)

Then,
W=p(mean value)*deltaV=(500/3)*(0.5^-12 - 2^-12)*1.5.

 

[cae20452]

yes so easily u can solve the question in the above i was going to write you that but saw already given
good luck pal