Question

A student increases the temperature of a 100 cm³ balloon from 60°C to 120°C. What will the new volume of the balloon be? 118 cm³ 200 cm³ 236 cm³ 400 cm³.

Answer 1

Volume is directly proportional to the temperature. The volume of the new balloon is given by: Option B: 200 cm³

What is the relation between volume and temperature for a gas?

If the initial volume and temperatures for a gas(assuming behaving ideally) are written as: $V_1$ and $T_1$, and the changed volume and temperatures are $V_2$ and $T_2$, then we have:

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

For the given case, we are provided that:

Volume of balloon at $T_1 = 60^\circ C$ is $V_1 = 100 \: \rm cm^3$

Let for temperature $T_2 = 120^\circ C$, we get volume of balloon (which is the volume of the air inside it) as $V_1 = x \: \rm cm^3$

Then, by the volume-temperature ratio, we get:

$\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}\\\\\dfrac{100}{60} = \dfrac{x}{120} \implies x = 2 \times 100 = 200 \: \rm cm^3$

Thus, the volume of the new balloon is given by: Option B: 200 cm³

Learn more about volume and temperature relation for ideal gases here:

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