Question

$0.02$ moles of an ideal diatomic gas with initial temperature ${20}^{o}C$ is compressed from $1500c{m}^3$ to $500c{m}^3$. The thermodynamic process is such that $P{V}^2=\beta$ where $\beta$ is a constant. Then the value of $\beta$ is close to:

(The gas constant, $R=8.31J/K/mol$)

• A. $7.5\times {10}^{-2}Pa.m^6$
• B. $1.5\times {10}^{2}Pa.m^6$
• C. $3\times {10}^{-2}Pa.m^6$
• D. $2.2\times {10}^{1}Pa.m^6$

Answer 1

The correct option is A $7.5\times {10}^{-2}Pa.m^6$

$P{V}^2=\beta$

and $PV=nRT$

$\therefore \beta =nRTV$

Putting the values as,

$n=0.02$

$T=293K$

$V=1.5\times {10}^{-3}{m}^3$

$\therefore \beta =7.5\times {10}^{-2}Pa.m^6$