Question

A gas undergoes a reversible adiabatic expansion. Identify the correct option about gas.
A. Energy increases
B. Pressure increases
C. Volume decreases
D. Temperature increases
E. Temperature decreases

Answer 1

Hint: We can use the first law of thermodynamics $Q = W + \Delta U$, where Q is the heat exchange, W is the work done and $\Delta U$ is the change in internal energy of the gas. Use the condition for adiabatic process i.e. the change in heat is zero ($Q = 0$). The dependence of internal energy on change in temperature is also useful. During expansion there is an increase in volume.

Complete step by step answer:
The first law of thermodynamics follows the law of conservation of energy according to which $Q = W + \Delta U$
Here, $Q$ is a change in heat, $U$ is the internal energy and $W$ is the work done.For an adiabatic process $Q = 0$. Therefore we get $\Delta U = - W$. Therefore for an adiabatic process the internal energy is a negative of work done.Work done is defined as $W = - P(\Delta V)$, where $P$ is the pressure and $\Delta V$ is the change in volume.

For expansion change in the volume is negative therefore the net work done will be positive.For the positive work the change in the internal energy is negative, which implies the final internal energy will be less than the initial internal energy.Using the relation,
\[\Delta U = n{C_P}\Delta T\]
We get that the change in temperature $\left( {\Delta T} \right)$ is directly proportional to change in internal energy $\left( {\Delta U} \right)$. So the final temperature decreases in comparison to the initial temperature i.e. temperature decreases.

Note:The most important point is to implement the condition for adiabatic process $Q = 0$. We should also ponder the relation between the change in temperature $\left( {\Delta T} \right)$ and the change in internal energy$\left( {\Delta U} \right)$. If in the question it is mentioned that the compression or expansion of the gas is rapid, then also the process is the adiabatic process. Due to sudden movement there is no chance of any heat entering or escaping from the system. Also, if in the question it is mentioned the gas used is real, then in that case we cannot make use of the ideal gas equation. Real gas does not follow any gas Laws.