Question

One mole of an ideal gas at $300K$ is expanded isothermally from an initial volume of 1 liter to 10 liters. The value of $\Delta E$ for this process is $(R = 2{\text{ cal mo}}{{\text{l}}^{ - 1}}{\text{ }}{{\text{k}}^{ - 1}})$
(A) $163.7cal$
(B) zero
(C) $138.1cal$
(D) $9{\text{ liter atm}}$

Answer 1

An isothermal process may be a thermodynamic process during which the temperature of a system remains constant. The transfer of heat into or out of the system happens so slowly that equilibrium is maintained. At a specific constant temperature, the change of a substance, object, or system is understood because of the Isothermal Process.

Complete answer:
In an ideal gas, all the collisions between molecules or atoms are perfectly elastic and no intermolecular force of attraction exists in an ideal gas because the molecules of an ideal gas move so fast, and they are so far away from each other that they do not interact at all. In the case of real gas, they have negligible intermolecular attractive forces. Ideal gas does not exist naturally. However, gases behave most ideally at high temperature and low-pressure conditions. The entire internal energy in an ideal gas is in the form of kinetic energy of the particles and any change in the internal energy results in a change of temperature.
Now using the formula for isothermal expansion which is $\Delta E = n{C_v}\Delta T$ we can find the value of $\Delta E$ but for isothermal process the value of $\Delta T$ is zero because it is constant for isothermal process so the value is $\Delta T = 0$ hence the value of $\Delta E$ is zero.
Hence our answer is option B.

Note:
If a system is in touch with a thermal reservoir from outside, then, to take care of equilibrium, the system slowly adjusts itself with the temperature of the reservoir through heat exchange. In contrast, in another phenomenon, no heat transfer occurs between a system and its surrounding. During this process, the temperature of the system is modified so as to keep the heat constant. This process is understood because of the natural process.