Question 866: Thermodynamics & KTG

Question

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled

Accepted Answer

The correct answer is
Option B: by increasing T to 2T
. Here's why:
The translational kinetic energy (KE) of gas molecules is directly proportional to the absolute temperature (T). This relationship is described by the following equation:
$$KE = \frac{3}{2} kT$$
Where:
KE is the translational kinetic energy
k is the Boltzmann constant
T is the absolute temperature in Kelvin
To double the translational kinetic energy, we need to double the absolute temperature. This means increasing T to 2T.
Let's analyze why the other options are incorrect:
Option A: Increasing T to 4T
would quadruple the translational kinetic energy, not double it.
Option C: Decreasing T to T/2
would halve the translational kinetic energy.
Option D: Increasing T to Ã¢ÂÂ2T
would increase the kinetic energy by a factor of Ã¢ÂÂ2, not double it.
Therefore, the only way to double the translational kinetic energy of gas molecules is to double the absolute temperature.

Answer

by increasing $$\mathrm{T}$$ to $$4 \mathrm{~T}$$

Answer

by increasing $$\mathrm{T}$$ to $$2 \mathrm{~T}$$

Answer

by decreasing $$\mathrm{T}$$ to $$\mathrm{T} / 2$$

Answer

by increasing $$\mathrm{T}$$ to $$\sqrt{2} \mathrm{~T}$$

Thermodynamics & KTG

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled

Choose the correct answer: