Question

For any gas the pressure coefficient ($\beta$) is equal to the volume coefficient ($\alpha$). This can be proved by:

• A. Charle's law
• B. Boyle's law
• C. Grahm's law
• D. Avogadro's number

Answer 1

The correct option is A Charle's law

If $V$ and $V_o$ are the volume of a gas at temperature $TK=t^{o}C$ and $273K=0^{o}C$ respectively. Using Charles law we get $\frac{V}{T}=\frac{V_o}{273}$
or
$V=V_o(\frac{T}{273})=V_o(\frac{273+t}{273})=V_o(1+\frac{t}{273})=V_o(1+\alpha t)$. ($\alpha$ is the volume coefficient)
Similarly using Gay Lussac's law we get
$P=P_o(\frac{T}{273})=P_o(\frac{273+t}{273})=P_o(1+\frac{t}{273})=P_o(1+\beta t)$. ($\beta$ is the pressure coefficient)
We have $\alpha =\beta =\frac{1}{273}$ for all gases.
And from these relations we see that at $t=-{273}^{o}C$ the volume and pressure of a gas becomes zero and thus temperature less than this is not possible.
We have used Charles law and Gay Lussacs law in deriving this and thus A is the right answer.