The correct option is (4) 12R.
We have given,
number of moles of gas = 4 mol
change in temperature = 3° c or 3 k
\(\therefore\) work done by gas = -pdv
= -p\(\int^{v2}_{v_1}dv\) (p = constant pressure)
= - p(v2 - v1)
= - p \(\left(\cfrac{MRT_2}p-\cfrac{nRT_1}p \right)\) (using ideal gas equation)
= - p x \(\cfrac{nR}p\) (T2 - T1)
= - 4 x R x ΔT
= - 4 x R x 3
= - 12 R
Hence, the work done by gas = 12 R.