Question

When the temperature of an ideal gas is increased from $27^{\circ} C$ to $927^{\circ} C$, the kinetic energy will be

• A. same
• B. eight times
• C. four times
• D. twice

Answer 1

Answer: (C)

Increase in temperature of ideal gas from $27^{\circ} C$ to $927^{\circ} C$
$\therefore $ Increase in $K E=\frac{3}{2} R T$
$T_{1}=27+273=300\, K$
$T_{2}=927+273=1200\, K$
$\therefore K E_{1}=\frac{3}{2} \times R \times 300\, K$
$K E_{2}=\frac{3}{2} \times R \times 1200\, K$
So, $\frac{K E_{2}}{K E_{1}}=\frac{\frac{3}{2} \times R \times 1200\, K}{\frac{3}{3} \times R \times 300\, K}=4$
Hence kinetic energy is increased four times.