At $4^{o} C$ , a gas occupies $200 m l$ and the same amount of gas at the same pressure occupies $300 m l$ at $144^{o} C$ . The absolute zero from this data is:

Open in App

Solution

Absolute zero is the temperature when the all motions of the gas molecules are zero i.e. temperature at which volume occupied is zero.
According to Charle's law: $V \propto T$ where $V$ is in $L$ and $T$ in $K$ .
$∴ V = m T + c$ where $m$ =slope of the $V T$ plot and $c$ =intercept.
At absolute zero $V = 0$
and $m = \frac{d V}{d T} = \frac{V_{2} - V_{1}}{T_{2} - T_{1}}$
Given that: $V_{1} = 0.2 L, T_{1} = 4^{\circ} C = 277 K$ and $V_{2} = 0.3 L, T_{2} = 144^{\circ} C = 417 K$
Upon substitution we get:
$m = \frac{0.3 - 0.2}{417 - 277} = \frac{0.1}{140}$
$m = 0.000714 L / K$
as $c = V_{1} - m T_{1} = 0.2 - 0.000714 \times 277$ = $0.0022 L$
Substituting the values of $m$ and $c$ in straight line equation at absolute zero we get:
$0 = 0.000714 \times T + 0.0022$
$T = - 3.168 K$ is the absolute zero for the system.

Suggest Corrections

Similar questions

250 m L

745 m m

H g

25^{o} C

200 m L

200 m L

0.820

20^{o} C

1.025

{d m}^{3}

300 m l

27^{o} C

730 m m

S T P

10 g

2

Join BYJU'S Learning Program