Figure below shows two paths that may be taken by a gas to go from a state A to a state C.

In process AB 400 J of heat is added to the system and  process BC, 100 J of heat is added to the system. The heat absorbed by the system in the process AC will be

For the process ABC,

${\mathrm{\Delta Q}}_{\mathrm{AB}}=400\mathrm{J}$

${\mathrm{\Delta Q}}_{\mathrm{BC}}=100\mathrm{J}$

$\therefore \mathrm{\Delta Q}=500\mathrm{J}$

$\mathrm{\Delta W}=\text{area under the curve}$

$=\text{area under }\mathrm{BC}$

$=(6\times {10}^4)\times (4\times {10}^{-3}-2\times {10}^{-3})=120\mathrm{J}$

From first law of thermodynamics

$\mathrm{\Delta }Q=\mathrm{\Delta }U+W$

$\Rightarrow \mathrm{\Delta U}=(500-120)\mathrm{J}$

$=380\mathrm{J}$

Since $\mathrm{\Delta }U$ is path independent , it is same for path AC too.

${\mathrm{\Delta W}}_{\mathrm{AC}}=\text{area under }\mathrm{AC}$

$=(\frac{1}{2}\times 2\times {10}^{-3}\times 4\times {10}^4)+(2\times {10}^{-3}\times 2\times {10}^4)$

$=80\mathrm{J}$

$\therefore \mathrm{\Delta }{Q}_{AC}=\mathrm{\Delta }U+\mathrm{\Delta }W$

$=380+80=460\mathrm{J}$