Question

If the temperature of 1 mole of a gas is increased by ${{50}^{\circ }}C$ the change in kinetic energy of the system will be:
A. 62.32 J
B. 6.235 J
C. 623.5 J
D. 6235.0 J

Answer 1

Hint: Kinetic energy of any object is the energy that is possessed by the object when it is in motion. It is found that temperature and kinetic energy are directly proportional to each other that is as the temperature increases the kinetic energy also increases.

Complete step by step solution:
-We know that energy is equal to: \[Energy=\dfrac{3}{2}RT\]
-We are being provided with value of $\Delta T=50K$,
So, we can write \[\Delta E=\dfrac{3}{2}R\left( \Delta T \right)\],
- The value of R is 8.314, now by putting all the given values in the above equation we get:
     \[\begin{align}
  & \Delta E=\dfrac{3}{2}\times 8.314\times 50 \\
 & =623.5J \\
\end{align}\]
So, we get the answer as 623.5J.
- Hence, we can conclude that the correct answer is option (C), that is 623.5J.

Additional Information: - It is found that all the objects have kinetic energy when they are moving, if there is no work done by the various forces that are present outside the system then it is found that the total energy of the system remains constant.
- And if the work is done on the system by other objects present in the surroundings, then the total energy of the system will change.
- Kinetic energy is found to be inversely proportional to the potential energy. That is, we can say that when the potential energy increases, the kinetic energy decreases.

Note: - We must not forget to write the unit of kinetic energy that is joule denoted by J, after solving any question.
- One must not get confused in between terms kinetic energy and potential energy, potential energy is the energy in a body due to its position, while kinetic energy is the energy in a body due to its motion.