Question

Correct gas equation is

• A. $\frac{V_1T_2}{p_1}=\frac{V_2T_1}{p_2}$
• B. $\frac{p_1T_2}{V_1}=\frac{p_2V_1}{T_2}$
• C. $\frac{p_1 V_1}{p_2 V_2}=\frac{T_1}{T_2}$
• D. $\frac{V_1 V_2}{T_1 T_2}=p_1 p_2$

Answer 1

The Correct Option is C

If temperature, volume and pressure of fixed
amount (say n mole) of a gas vary from $T_1, V_1 \,and \,p_1$
to $T_2, V_2\, and\, p_2$ respectively. Then, ideal gas
equation for two states can be written as
$\, \, \, \, \, \, \, \, \, \, p_1 V_1=n RT_1 \, \, \, \, or\, \, \, \, \frac{p_1V_1}{T_1}=nR\, \, \, \, \, \, \, ...(i)$
$\, \, \, \, \, \, \, \, \, \, p_2 V_2 = n RT_2 \, \, \, \, or\, \, \, \, \frac{p_2V_2}{T_2}=nR\, \, \, \, \, \, \, ...(ii)$
On combining Eqs. (i) and (ii), we get
$\, \, \, \, \, \, \, \, \, \, \frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}$
or $\, \, \, \, \, \, \, \, \, \, \frac{p_1V_1}{p_1V_2}=\frac{T_1}{T_2}$
So, it called combined gas equation.