# A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is :Option 1)$130 J$Option 2)$100J$Option 3)$140J$Option 4)$120J$

Process abca is cyclic process.

$\Rightarrow \triangle Uabca=0$

$\Rightarrow \triangle Uabc+\triangle Uca=0$

$\Rightarrow \triangle Uabc-180=0$

$\triangle Uabc=180J$

Now according to $I^{st}$ has of thermodyamics

$\triangle Q=\triangle U +\triangle W$

$\Rightarrow \triangle W_{abc}= \triangle Q_{abc}-\triangle U_{abc}$

$=(250+60)-180$

$\triangle W_{abc}=130J$

Option 1)

$130 J$

Option 2)

$100J$

Option 3)

$140J$

Option 4)

$120J$

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