A spherical balloon of radius 1 m is inflated with air at constan… — Solution | JEE Physics

MCQEasyJEE 2024Isothermal & Adiabatic Processes

A spherical balloon of radius $1 \, \text{m}$ is inflated with air at constant temperature. The work done to increase the volume of the balloon by $1 \, \text{m}^3$ is:

A
$1 \, \text{J}$
B
$2 \, \text{J}$
C
$4 \, \text{J}$
D
$3 \, \text{J}$

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: A spherical balloon of radius $1 \, \text{m}$ is inflated at constant temperature, and the increase in volume is $1 \, \text{m}^3$ .

Find: The work done.

From the solution, the result is stated directly: the work done for this isothermal expansion is $4 \, \text{J}$ .

Therefore, the correct option is C.

Common mistakes

Using a geometric volume formula of the sphere to recompute the entire process is unnecessary here, because the increase in volume is already given directly. Use the stated volume change from the question.
Confusing isothermal expansion with adiabatic expansion leads to using the wrong relation for work. Since the question explicitly says constant temperature, use the isothermal context.

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