Chapter A.9, Problem 110AYU

To determine

To find: For a certain ideal gas, the volume V (in cubic centimeters) equals 20 times the temperature T (in degrees Celsius). If the temperature varies from $80°$ to $80°\text{C}$ inclusive, what is the corresponding range of the volume of the gas.

Answer to Problem 110AYU

The volume V of the gas varies from $1600$ cubic centimetre to $2400$ cubic centimetre.

Explanation of Solution

Given that the volume $\text{V}$ equals $20$ times the temperature $\text{T}$.

$\text{i}.\text{e}., \text{V} = 20\text{T}$

$\Rightarrow \text{T} = \frac{\text{V}}{20}$   -----(1)

Also given that the temperature varies from $80°\text{C}$ to $120°\text{C}$ inclusive.

$\text{i}.\text{e}., 80°\text{C} \le \text{T} \le 120°\text{C}$

$80°\text{C} \le \frac{\text{V}}{20} \le 120°\text{C}$   -----(By (1))

$80°\text{C}\times 20 \le \frac{\text{V}}{20}\times 20 \le 120°\text{C}\times 20$   -----(Multiplied each sides by $20$)

$1600 \le \text{V} \le 2400$   -----(Simplify)

∴ The volume V of the gas varies from $1600$ cubic centimetre to $2400$ cubic centimetre.