Question

Does the volume of a fixed quantity of gas decrease to half its original value when the temperature is lowered from 100 ∘c to 50 ∘c ?

Answer 1

Answer:

No

Explanation:

Let's assume the gas pressure is constant. Then we can use Charle's law, which states that the volume of the gas is proportional to the absolute temperature (in Kelvin):

$\frac{V}{T}=const.$

This can be rewritten as

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

where we have

$T_1 = 100^{\circ}+273 =373 K$  is the initial temperature of the gas

$T_2 = 50^{\circ}+273 =323 K$  is the final temperature of the gas

Re-arranging the previous equation, we find

$V_2=V_1 \frac{T_2}{T_1}=V_1 \frac{323 K}{373 K}=0.87 V_1$

so, the volume of the gas decreases by a factor 0.87.