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Standard XII

Physics

Equipartition Theorem

In a certain ...

Question

In a certain gas $\frac{2}{5}$ th of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. How much energy must be supplied to one mole of this gas at constant volume to raise the temperature by $1^{\circ} C$ ?

20.8 J

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28.8 J

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26.8 J

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25.8 J

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Solution

The correct option is A $20.8 J$
Since two fifth energy is associated with the rotation, thus there are five degrees of freedom out of which two are rotational and three translational.

Thus $e_{t o t a l} = \frac{5}{2} R T$

$Δ E = \frac{5}{2} (8.314) 1 = 20.8 J$

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Similar questions

Q. In a certain gas

\frac{2}{5}

th of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. The average translation energy of one such molecule, when the temperature is

27^{\circ} C

is given by

x \times 10^{- 23} J

,then find

x

For the theory of equipartition of energy the energy associated with the each molecule is f/ 2 KT if the gas has n number of moles , now how we can convert the moles into molecules and the energy associated with total molecule is found to be n×na×f/2KT. Here na×K=R(gas constant) how? And total energy associated with total molecule is n ×R×T×f/2.

Q. How much heat energy must be supplied to 14 g of nitrogen gas at room temperature to raise its temperature by

40^{\circ} C

at a constant pressure?

Q. Heat energy of

743 J

is needed to raise the temperature of

5

moles of an ideal gas by

2 K

at constant pressure. How much heat energy is needed to raise the temperature of the same mass of the gas by

2 K

at constant volume?

Q. A diatomic gas is heated at constant volume. If heat supplied to gas is Q, find the change in rotational kinetic energy of diatomic gas molecules.

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In a certain gas 25th of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. How much energy must be supplied to one mole of this gas at constant volume to raise the temperature by 1∘C?

The correct option is A 20.8JSince two fifth energy is associated with the rotation, thus there are five degrees of freedom out of which two are rotational and three translational.Thus etotal=52RTΔE=52(8.314)1=20.8J

In a certain gas $\frac{2}{5}$ th of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. How much energy must be supplied to one mole of this gas at constant volume to raise the temperature by $1^{\circ} C$ ?

The correct option is A $20.8 J$
Since two fifth energy is associated with the rotation, thus there are five degrees of freedom out of which two are rotational and three translational.

Thus $e_{t o t a l} = \frac{5}{2} R T$

$Δ E = \frac{5}{2} (8.314) 1 = 20.8 J$