Question

find the change in kinetic energy of one mole of ideal gas when temperature changes by 50 degree Celsius​

Answer 1

The change in kinetic energy of one mole of ideal gas when temperature changes by 50 degree Celsius​ is 1247.1 J/mol.

Explanation:

The given data is as follows.

             $T_{1}$ = 273 K

             $T_{2}$ = (50 + 273) K = 373 K

It is known that the relation between change in kinetic energy and change in temperature is as follows.

           $\Delta K.E = \frac{3}{2}K \Delta T$

For 1 mole of a gas the formula is $\Delta K.E = \frac{3}{2}R \Delta T$

Putting teh given values into the above formula as follows.

          $\Delta K.E = \frac{3}{2}R \Delta T$

                     = $\frac{3}{2} \times 8.314 J/mol K \times (373 - 273) K$

                     = 1247.1 J/mol

Therefore, the change in kinetic energy of one mole of ideal gas when temperature changes by 50 degree Celsius​ is 1247.1 J/mol.

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Answer 2

The Kinetic gas equation is :

PV = 1/3mnUrms²

Here

P is pressure on the gas ,

V is the volume occupied ,

m be the mass of the gas molecule ,

n is number of moles of the gas and Urms² is the root mean square Velocity.

Also:-

Kinetic energy (K.E) of n moles of a gas = n×3/2RT

Change in kinetic energy (K.E) = Kf - Ki

As the formula for K.E is 3/2RT.

Therefore:-

According to the question,

➨ K.E = 3/2 R(T+50)-3/2RT

➨ K.E = 3/2R(T - T+50) J

➨ K.E = 3/2× 8.314×50 J

➨ K.E = 623.55 J