Question

An ideal gas mixture filled inside a balloon expands according to the relation ${\mathrm{PV}}^{2/3}$ = constant.The temperature inside the balloon will be:

• A. Constant
• B. Increasing
• C. Decreasing
• D. Cannot be defined

Answer 1

The correct option is B

Increasing

Explanation for correct option:

(b) Increasing

• At ambient temperatures, it is liquid.
• $$\begin{gathered} {\mathrm{PV}}^{2/3}=\mathrm{Constant} \\ \frac{\mathrm{nRT}}{\mathrm{V}}{\mathrm{V}}^{2/3}=\mathrm{constant} \\ \frac{\mathrm{T}}{{\mathrm{V}}^{1/3}}=\mathrm{constant} \\ \mathrm{T}=\left(\mathrm{k}\right){\mathrm{V}}^{1/3} \end{gathered}$$
• Since the temperature is directly proportional to the volume
• So increase in volume also indicates an increase in temperature.
• Hence this is the correct option.

Explanation for incorrect options:

(a) Constant

• Since the temperature is directly proportional to the volume
• So increase in volume also indicates an increase in temperature.
• so the temperature does not remain constant.
• Hence this is the incorrect option.

(c ) Decreasing

• Since the temperature is directly proportional to the volume
• So increase in volume also indicates an increase in temperature.
• so the temperature does not remain decrease.
• Hence this is the incorrect option.

(d) Cannot be defined

• Since the temperature is directly proportional to the volume
• So increase in volume also indicates an increase in temperature.
• Hence this is the incorrect option.

So option (b) Increasing is the correct answer.