Question

pressure p and volume v of a gas are related by the law p(v^u)=k where u and k are constants.Find the rate of pressure with time.

Answer 1

dp/dt= -k/(v^2u)

Answer 2

how?

Answer 3

Does your original equation look like this?
\[pv ^{u} = k\]

Answer 4

@ranga ,yes!

Answer 5

First multiply both sides by:
\[v ^{-u}\]

Answer 6

Then find dp/dt

Answer 7

i used the rules
Btw i'm nt sure about it

Answer 8

But if i multiply throughout by v^-u
im left with;
\[p=k v ^{-u}\]
P is still not varying with 't'
so how can i find dp/dt?

Answer 9

@Ahmad1919 ,thanks for giving it a try,buddy!

Answer 10

if f(x) = a/b^k f'(x) = -a/b^2k it's a rule
and ur wlc

Answer 11

oh!
thanks!

Answer 12

*yet again,haha

Answer 13

@kesh,
\[p = kv ^{-u}\]
\[\frac{ dp }{ dt } = k(-u)v ^{-u-1}\frac{ dv }{ dt}\]
\[\frac{ dp }{ dt} = \frac{ -ku }{ v ^{u+1}}\frac{ dv }{ dt }\]

Answer 14

Thank you so much @ranga !