Question

Which of the following relationships is valid?

• A. $\frac{pV}{T}=\frac{2}{3}K$
• B. $\frac{pV}{T}=\frac{3}{2}K$
• C. $\frac{pV}{T}=2K$
• D. $\frac{pV}{T}=3K$

Answer 1

Answer: (A)

$\frac{pV}{T}=\frac{2}{3}K$

$pV=\frac{1}{3}mN{C}_2$ ($mN=$ molar mass)

For 1 mole of gas pV=RT, n=N(Av. constant)

$RT=\frac{1}{3}mN{C}_2$

$RT=\frac{2}{3}\times \frac{1}{2}mN{c}_2$

$=\frac{2}{3}$K

So, $pV=\frac{2}{3}$K

$C=$ Speed of molecule

$p=$ Pressure

$V=$ Volume

$R=$ Gas constant

$T=$ Temperature

$n=$ No. of moles

$m=$ Molar mass