Question

The average force applied on the walls of a closed container depends on temperature (T) as (T is the temperature of an ideal gas)

• A. \(T^2\)
• B. \(T^3\)
• C. \(T^1\)
• D. \(T^{-1}\)

Hint:

Fixed volume means pressure is proportional to T.

Answer 1

The Correct Option is C

Step 1: Kinetic theory:
$P=\dfrac13\dfrac{N}{V}m\overline{v^2}$ and $\overline{v^2}\propto T$.

Step 2: Closed container:
$N$ and $V$ do not change, so $P\propto T$.

Step 3: Force:
$F=PA$, with $A$ fixed. So $F\propto T$.

Final Answer:
At fixed volume pressure rises linearly with temperature. \[ \boxed{C} \]