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

$Assertion :$ The isothermal curves intersect each other at a certain point.
$Reason :$ The isothermal change takes place slowly,so,the isothermal curves have very little slope.

The condition $dw = dq$ holds good in the following process:

Work done per mole in an isothermal change is

$A$ certain gas is isothermally compressed to $(1/3)^{rd}$ of its initial volume $(V_0 = 3 \ \text{L})$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5 \ \text{N/m}^2$,the magnitude of work done on the gas is . . . . . . $J$.

$A$ certain amount of heat supplied to an ideal gas under isothermal conditions will result in: