The resistance of an electrolyte varies with temperature T as RT $$=$$ $$R01+$$αT, where $$R0$$ and α are constants. A constant potential difference V is applied to the two electrodes (each$$ of surface area $$A) which are dipped in this electrolyte. If $$T0$$ it the temperature of the surroundings, the loss of heat to the surroundings per unit surface area per unit time is governed by the same relation $$H=kT$$−$$T0A$$, then the steady state temperature is

Question

The resistance of an electrolyte varies with temperature T as RT $$=$$  $$R01+$$αT, where $$R0$$ and α are constants. A constant potential difference V is applied to the two electrodes (each$$ of surface area $$A) which are dipped in this electrolyte. If $$T0$$ it the temperature of the surroundings, the loss of heat to the surroundings per unit surface area per unit time is governed by the same relation $$H=kT$$−$$T0A$$, then the steady state temperature is

Infinity Learn · Accepted Answer

Power generated in the resistance is being lost in the environment.At steady state, $$V2RT$$ $$=$$ kT−$$T0AGiven$$ R $$=$$  $$R01+$$αT,  $$V2R01+$$αT $$=$$ kT−$$T0A$$,T−$$V2$$α$$R0$$ $$+kA$$ $$=$$ $$V2$$α$$R0$$ $$+kAT0$$,  $$T=V2+kAR0TkR0A$$−α$$V2$$

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