Abstract: Based on the current of quantized mesoscopic RLC electric circuit can product the Jonue heat, quantum effects should be taken into account at finite temperature.In the equilibrium state of thermo environment,expected value of any mechanical quantity can be described by the ensemble average energy.Furthermore,using the technique of integration within ordered product(IWOP) of operator ,the thermo vacuum state was obtained in a quantized mesoscopic RLC electric circuit for the first time.Finally, by means of theoretical calculation, expected value of pure state at thermo vacuum state was used to replace the ensemble average energy ,which stored in the LC element and consumed in the R element.

Key words: quantum optics, quantized mesoscopic RLC electric circuit, thermo vacuum state；expected value