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

Answer:

B.$p(v)=\frac{320}{v}$

Step-by-step 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)$\propto\frac{1}{v}$

$p(v)=\frac{k}{v}$

Where k=proportionality constant

Substitute the given values then, we get

$8=\frac{k}{40}$

$k=8\times 40=320$

Substitute the value of k then, we get

$p(v)=\frac{320}{v}$

Hence,option B is true.

Answer 2

Answer:

B

Step-by-step explanation:

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

p = $\frac{k}{v}$ ← k is the constant of variation

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

k = pv = 8 × 40 = 320

⇒ p(v) = $\frac{320}{v}$ → B