Question

On a ship sailing in the Pacific ocean, where the temperature is 23.4${}^{\circ }$C, a balloon is filled with 2 L air. What will be the volume of the balloon when the ship reaches the Indian ocean where the temperature is 26.1${}^{\circ }$C ?

• A. 2.0184 L
• B. 1.96 L
• C. 1.88L
• D. 2.42 L

Answer 1

The correct option is A

2.0184 L

This question deals with changes in volume of a gas with change in temperature, with the pressure remaining constant.

This is dealt by Charles' law which states that pressure remaining constant, volume of a gas is directly proportional to its temperature.

i.e $V$ α $T$ or $\frac{V}{T}=k$, where $k$ is a constant.

Thus, $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, where $V_{1}and{T}_1$ refer to the initial volume and temperature respectively where as $V_{2}and{T}_2$ refer to the final volume and temperature respectively.

$V_1$ = 2 L, $V_2$ = ?

$T_1$ = 273 + 23.4 = 296.4K
$T_2$ = 273 + 26.1 = 299.1K

Therefore, $V_2=\frac{V_1\times T_2}{T_1}$= $\frac{2\times 299.1}{296.4}$ = 2.01842 L