For an isothermal expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to:

$A$ gas is compressed at constant temperature. Its molecules gain:

Write the first law of thermodynamics for an isothermal expansion process.

Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The masses of gas in $A$ and $B$ are $m_A$ and $m_B$,respectively. The gases are allowed to expand isothermally to the same final volume $2V$. The changes in pressures of the gas in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$,respectively. Then

$A$ vertical cylinder with heat-conducting walls is closed at the bottom and is fitted with a smooth light piston. It contains one mole of an ideal gas. The temperature of the gas is always equal to the surrounding's temperature,$T_0$. The piston is moved up slowly to increase the volume of the gas to $\eta$ times. Which of the following is incorrect?

Heat is given to an ideal gas in an isothermal process.
$A.$ Internal energy of the gas will decrease.
$B.$ Internal energy of the gas will increase.
$C.$ Internal energy of the gas will not change.
$D.$ The gas will do positive work.
$E.$ The gas will do negative work.
Choose the correct answer from the options given below: