Question

A certain gas is taken to the five states represented by dots in the graph. The plotted lines are isotherms. Order of the most probable speed $v_p$ of the molecules at these five states is

• A. $V_{pat3}>V_{pat1}=V_{pat2}>V_{pat4}=V_{pat5}$
• B. $V_{pat1}>V_{pat2}=V_{pat3}>V_{pat4}=V_{pat5}$
• C. $V_{pat3}>V_{pat2}=V_{pat4}>V_{pat1}=V_{pat5}$
• D. Insufficient information to predict the result.

Answer 1

The correct option is A $V_{pat3}>V_{pat1}=V_{pat2}>V_{pat4}=V_{pat5}$

The given $p-v$ graph represents three isotherms.
For the uppermost isotherm, temperature will be highest.
$\Rightarrow T_a>T_b>T_c$


Points (1, 2) lie on isotherm b
$\Rightarrow T_1=T_2=T_b$
Points (4, 5) lie on on isotherm 'c'
$\Rightarrow T_4=T_5=T_c$
Hence order of temperature,
$T_3>T_1=T_2>T_4=T_5$
The most probable spead of gas molecules,
$v_p\propto \sqrt{T}$
$\Rightarrow V_{p_3}>V_{p_1}=V_{p_2}>V_{p_4}=V_{p_5}$