Rates of change

[cornish_socialist]

Ok, i've got this question on a test maths paper and i've tried answering it but i can't work out what part of it means. I looked at the mark scheme on line to see if that would help with how to work it out but it just lists the answer (it's only 2 marks).

When the gas in a balloon is kept at a constant temperature, the pressure P in atmospheres and the
volume V m^3 are related by the equation:
P =K/V

where k is a constant. [This is known as Boyle’s Law.]
When the volume is 100m^3, the pressure is 5 atmospheres, and the volume is increasing at a rate of
10m^3 per second.

ii) Find dP/dV in terms of V

What does that mean; "in terms of v?"

Thanks,

( k is 500 by the way, worked out in part i. )

 

[Deleted member 4993]

Ok, i've got this question on a test maths paper and i've tried answering it but i can't work out what part of it means. I looked at the mark scheme on line to see if that would help with how to work it out but it just lists the answer (it's only 2 marks).

When the gas in a balloon is kept at a constant temperature, the pressure P in atmospheres and the
volume V m^3 are related by the equation:
P =K/V

where k is a constant. [This is known as Boyle’s Law.]
When the volume is 100m^3, the pressure is 5 atmospheres, and the volume is increasing at a rate of
10m^3 per second.

ii) Find dP/dV in terms of V

What does that mean; "in terms of v?"

in terms of V - means as a function of V or you need to find

\(\displaystyle \frac{dP}{dV} \ = \ f(V)\)

You can also do this directly (without dealing with 'time' as a variable)

\(\displaystyle P \ = \ \frac{K}{V}\)

\(\displaystyle \frac{dP}{dV} \ = \ - \ \frac{K}{V^2}\)

and that's it....


Thanks,

( k is 500 by the way, worked out in part i. )

 

[cornish_socialist]

Oh I get it now!

I asked my physics teacher and my maths teacher and I still didn't get it, and then I looked at your reply and I still didn't and then it clicked after I reread it a couple of times.

Thank you!

 

[Deleted member 4993]

Oh I get it now!

I asked my physics teacher and my maths teacher and I still didn't get it, and then I looked at your reply and I still didn't and then it clicked after

I reread it a couple of times. <<< That's a very good habit - cultivate it.

Thank you!