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 $KE=\frac{3}{2}RT$
$T_1=27+273=300K$
$T_2=927+273=1200K$
$\therefore K{E}_1=\frac{3}{2}\times R\times 300K$
$K{E}_2=\frac{3}{2}\times R\times 1200K$
So, $\frac{K{E}_2}{K{E}_1}=\frac{\frac{3}{2}\times R\times 1200K}{\frac{3}{3}\times R\times 300K}=4$
Hence kinetic energy is increased four times.