Question

The pressure of a gas p(v) varies inversely with the volume of gas v. the pressure of a gas measures 8kg/cm^2 when its volume is 40cm^3.

which equation can be used to find the pressure of the gas when its volume is changed.

A. p(v)=320v
B. p(v)=320 over v
C. p(v)=5v
D. p(v)=5 over v

Answer 1

B.
`p(v)=(320)/(v)`

Explanation:

We are given that

The pressure of gas p(v) varies inversely with the volume of gas v.

Pressure of gas measures=
`8kg/cm^3`

Volume of gas=
`40cm^3`

We have to find the equation that can be used to find the pressure of the gas when its volume is changed.

According to question

p(v)
`\propto(1)/(v)`

`p(v)=(k)/(v)`

Where k=proportionality constant

Substitute the given values then, we get

`8=(k)/(40)`

`k=8* 40=320`

Substitute the value of k then, we get

`p(v)=(320)/(v)`

Hence,option B is true.

Answer 2

B

Explanation:

Since p and v vary inversely then the equation relating them is

p =
`(k)/(v)` ← k is the constant of variation

to find k use the condition p = 8 when v = 40

k = pv = 8 × 40 = 320

⇒ p(v) =
`(320)/(v)` → B