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In a certain gas 2/5th of the energy of molecule is associated with the rotation of molecules and rest of it is associated with the motion of center of mass. Identify
correct option(s). (𝑘_B = 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑅 = 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑎𝑙 𝑔𝑎𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

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Avg translational KE of one such molecule when temperature is 27 °C is $450 k_{B} J$

Avg translational KE of one such molecule when temperature is 27 °C is $500 k_{B} J$

Energy that must be supplied to one mole of such gas to increase its temperature by 1 °C is $2.5 R J$

Energy that must be supplied to one mole of such gas to increase its temperature by 1 °C is $3 R J$

answer is A, C.

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Detailed Solution

2/5th of the total kinetic energy of a molecule is rotational kinetic energy.

⇒ Translational degrees of freedom = 3 and rotational degrees of freedom = 2

⇒ 𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝐾𝐸 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒 $= \frac{3}{2} k_{B} T = \frac{3}{2} \times 300 \times k_{B} = 450 k_{B} J$

Energy to be supplied to 𝑛 moles of ideal gas to increase its temperature by Δ𝑇 is given by

$E = {nC}_{V} ΔT = n \frac{f}{2} RΔT = 1 \times \frac{5}{2} \times R \times 1 = 2.5 RJ$

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