$A$ container that suits the occurrence of an isothermal process should be made of

$A$ 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?

$A$ cylinder fitted with a piston contains $0.2 \, moles$ of air at a temperature of $27^{\circ}C$. The piston is pushed so slowly that the air within the cylinder remains in thermal equilibrium with the surroundings. Find the approximate work done by the system if the final volume is twice the initial volume (in $J$).

$Assertion :$ In an isothermal process,the whole of the heat supplied to the body is converted into internal energy.
$Reason :$ According to the first law of thermodynamics,$\Delta Q = \Delta U + P\Delta V$.

If the pressure of an ideal gas is decreased by $10 \%$ isothermally,then its volume will

One mole of an ideal gas expands from an initial volume of $10 \; L$ to a final volume of $20 \; L$ at a constant temperature of $300 \; K$. Calculate the work done by the gas in $J$. $(R = 8.31 \; J/mol \cdot K)$ (in $; J$)