Question

In adiabatic process is u=ncvdt valid?

• A. Yes
• B. No

Answer 1

Answer: (A)

Yes

Answer 2

The internal energy ($U$) of an ideal gas depends solely on its temperature. The change in internal energy ($\Delta U$) for an ideal gas is always given by the formula:

$$\Delta U = nC_v \Delta T$$

where:

• $n$ is the number of moles of the gas.
• $C_v$ is the molar specific heat capacity at constant volume.
• $\Delta T$ is the change in temperature.

This formula is a fundamental definition of the change in internal energy for an ideal gas and is valid for any thermodynamic process (isothermal, isobaric, isochoric, adiabatic, etc.) as long as the gas is ideal.

An adiabatic process is defined by no heat exchange with the surroundings ($Q=0$). According to the first law of thermodynamics, $\Delta U = Q - W$. For an adiabatic process, this simplifies to $\Delta U = -W$.

Since $\Delta U = nC_v \Delta T$ is always true for an ideal gas, it remains valid in an adiabatic process. Combining this with the first law for an adiabatic process, we get:

$$nC_v \Delta T = -W$$

This shows that the work done in an adiabatic process directly changes the internal energy (and thus the temperature) of the system.

Therefore, assuming 'u' refers to $\Delta U$ and 'dt' refers to $\Delta T$, the expression $\Delta U = nC_v \Delta T$ is valid for an adiabatic process involving an ideal gas.