Question
Can a system be heated and its temperature remains constant?

Answer

If the system does work aganist the surrounding so that it compensates for the heat supplied, the tempreature can remain constant.
It is given that $\Delta\text{T}=0\Rightarrow\Delta\text{U=0}$
$\therefore\Delta\text{Q}=\Delta\text{U}+\Delta\text{W}$  
$\Rightarrow\Delta\text{Q}=\Delta\text{W}$ so heat supplied to the system is utilized in expansion system is isothermal.

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