1. Calculation of body heating due to external radiation:

To calculate the increase in temperature that will be caused by the radiation power, while having the radiation density, you need to know the surface area of the object. To find the surface area of a person, we will use the Mosteller formula:

where m – body mass (kg) and h – height (cm).

According to the formula, the surface of body is:

Changes in temperature during everyday exposure:

Since I live in the Russian Federation, we will use the Russian standard for calculation:

Pmax = 10  W/cm²

Taking into account the specified power density level:

The power acting on the body

The heat generated by the body due to radiation:

where P – power, t – time.

Generated heat:

The heat generated by heating the body:

where c – specific heat capacity, m – mass, ΔT – temperature change.

Specific heat capacity of human body:

c = 3450 J/kg*K

According to formula (), the change in body temperature is:

Then:

Changes in temperature in production:

Maximum radiation power density in production:

P_max = 200 μW/cm²

Taking into account the specified power density level:

The power acting on the body

The heat generated by the body due to radiation:

The change in body temperature in production according to the formula is equal to:

Thus:

Thus, during production, the body heats up almost 7 times more than in everyday life.

The heat loss in this process will be used to radiate the body into the external environment in order to cool the body.

2. Counting the number of microwave radiation quanta for heating:

The frequency of microwave radiation:

f = 300 GHz

Heat generated by irradiation:

Where W₁ – the energy of 1 quantum W₁=h*f, n – number of heating quanta.

Then:

For everyday life:

For in production time:

Thus:

The number of quanta required to heat to the same heat is in the same ratio.

Answer:

Body temperature change in everyday life: 

Body temperature change in production: 

The number of quanta for heating in everyday life:   

The number of quanta for heating in production:

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Task 3

3. Compare numerically 2 typical devices: vacuum and semiconductor according to the following parameters:

   1. The maximum velocity of charged particles.

   2. The length of the interaction region for the angle of π-radian.

   3. Volumetric charge density.

   4. Calculate the microperviance, the «plasma» frequency for the vacuum device.

   5. For semiconductor: Debye length, plasma frequency. Material: Silicium.

Compare the values in clauses 3.4. and 3.5. Explain the difference in physical processes in both variants.

Given:

Parameters of the vacuum device: current 160 mA, accelerating voltage

5,6 kV, flow diameter 12 mm.

Parameters of the semiconductor device: Doping level 8∙10¹⁶ cm^-3, voltage 20 V, current channel thickness 1 microns.

The operating frequency of the devices is 14 GHz.

The operating temperature is 308 K.

Solving:

1. The maximum velocity:

   1. Vacuum device:

The maximum velocity of charged particles:

where q – electron charge, U_v – accelerating voltage, m – electron mass

According the formula:

2. Semiconductor:

Field strength:

The maximum speed corresponds to the saturation current:

Thus:

Maximum velocity of charged particles in a vacuum device is 444 times greater than in a semiconductor device.

2. The length of the interaction region for the angle of π-radian:

   1. Vacuum device:

The formula of the span angle:

where f – frequency; l_VAC - the length of the interaction area; V_V - flight speed.

The length of the interaction area:

2. Semiconductor:

Thus:

The ratio of the lengths of the interaction regions of devices is the same number

3. Volumetric charge density.

   1. Vacuum device:

From the formula for the current strength:

where n_V - bulk charge density; S - the cross-sectional area of the electron beam.

Thus:

2. Semiconductor:

In a semiconductor device, the bulk charge density is determined by the doping level:

Thus:

The charge density in a semiconductor is 8 times higher than in a vacuum device.

4. Calculating the microperviance, the «plasma» frequency for the vacuum device:

Calculation of the microperveance by the formula:

Thus:

Calculation of the «plasma» frequency by the formula:

Then we get:

5. Calculation of the Debye length and plasma frequency for a semiconductor device:

The formula for the Debye length:

Then:

Calculation of the plasma frequency:

Thus:

The frequency of plasma oscillations in a semiconductor is 20,000 times higher than in a vacuum device.

The characteristics of vacuum and semiconductor devices make it clear that it's impossible to say which is "better." Each has its own advantages, and therefore both can be used for specific purposes. Vacuum devices have the advantage of maximum carrier velocity and interaction region length, which allows for more efficient use of such devices as high-power microwave transmitters and klystrons. The higher carrier density and plasma frequency allow for more efficient use of semiconductor devices for integrated circuits and operation at terahertz frequencies.

Answer:

Table 2 – Calculated parameters of 2 devices

Parameters	Vacuum device	Semiconductor	Ratio of quantities
Maximum velocities, m/s
Length of the interaction region, m
Bulk charge density, m-3
Plasma frequency, rad/s
Microperviance		-	-
Debye length, m	-		-