Question

1 mole of an ideal gas in a cylindrical container have the P-V diagram as shown in figure. If V2 = 4V1, then the ratio of temperatures will be

• A. $\frac { 1 } { 2 }$
• B. $\frac { 1 } { 4 }$
• C. $\frac { 3 } { 2 }$
• D. $\frac { 3 } { 4 }$

Answer 1

Answer: (A)

$\frac { 1 } { 2 }$

Answer 2

: Ideal gas equation,

$P V = n R T$ Or $T = \frac { P V } { n R }$….. (i)

According to question

$P V ^ { 1 / 2 } =$ constant (1)

Multiplying both side by $\sqrt { V }$

Or $P V = A \sqrt { V }$….. (ii)

Form equation (i) and (ii)

$\therefore T = \frac { A \sqrt { V } } { n R } \Rightarrow T \propto \sqrt { V }$

Now $\frac { T _ { 1 } } { T _ { 2 } } = \sqrt { \frac { V _ { 1 } } { V _ { 2 } } } = \sqrt { \frac { V _ { 1 } } { 4 V _ { 1 } } } = \frac { 1 } { 2 } \quad \left[ \because V _ { 2 } = 4 V _ { 1 } \right]$

$\therefore \frac { T _ { 1 } } { T _ { 2 } } = \frac { 1 } { 2 }$