Question

Which of the following statement is true for a thermodynamical system where $∆U$ is the increase in internal energy and $∆W$ work done respectively?

• A. $∆U=-∆W$ in isothermal process
• B. $∆U=∆W$ in isothermal process
• C. $∆U=-∆W$ in an adiabatic process
• D. $∆U=∆W$ in an adiabatic process

Answer 1

The correct option is C

$∆U=-∆W$ in an adiabatic process

Explanation of correct option:

In an adiabatic process, no heat energy enters or leaves the system

$\Rightarrow ∆Q=0$

From the first law of thermodynamics

$$\begin{gathered} ∆Q=∆U+∆W \\ ∆U=-∆W \end{gathered}$$

Therefore for the adiabatic process, $∆U=-∆W$

Explanation of incorrect options:

Isothermal process: It is a thermodynamic process in which temperature remains constant.

In an isothermal process,

$∆U=0$, i.e., the internal energy is constant in an isothermal process.

From the first law of thermodynamics

$$\begin{gathered} ∆Q=0+∆W \\ ∆Q=∆W \end{gathered}$$

Hence, option C is correct.