The temperature of a gas is –78°C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2K is

Engineering

Physics

Degree of Freedom Internal Energy of Gas and Specific Heat Capacity of Gases

Question

–39°C

127°C

–78°C

117°C

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$E = \frac{3}{2} KT$

$\frac{E_{1}}{E_{2}} = \frac{T_{1}}{T_{2}}$

$\frac{K}{2 K} = \frac{T_{1}}{T_{2}}$

T₂ = 2T₁

T₁ = –78 + 273 = 195 K

T₂ = 2 × 195 k = 390 K

t₂ °C = 390 – 273 = 117°C