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Suppose $a,b,c$ are measured in meters. Then the semiperimeter $s=\dfrac{a+b+c}2$ is also given in meters, so $s-a,s-b,s-c$ are all also given in meters. When multiplied together, $(s-a)(s-b)(s-c)$ is measured in cubic meters. Divide this by $s$ , measured in meters, and this reduces to square meters. Take the square root and you end up back with meters once again. So the formula is indeed dimensionally consistent.

6 0

4 years ago

A gas is placed inside a very cold box. The gas molecules transfer heat to the walls of the box. Which best describes what happe

STatiana [176]

Answer:

the gas molecules slow down, and some change phase to liquid.

Explanation:

1) The heat always travels from the warmer substance to the coleer substace.

That is why it is correctly indicated that the gas molecules transfer heat to the walls of the box.

2) As this happens, means that the gas molecules lose heat energy and is cooled.

3) KInetic energy is directly related with the temperature: therefore, the lower the temperature the lower the kinetic energy.

4) Kinetic energy is, also, directly related to the square of the speed. So, the lower the kinetic energy, the lower the average speed of the molecules.

That is why it is correct to say that the gas molecules slow down.

5) Since it is said that the walls of the box are very cold, it may well happen that the energy passed from the molecules to the walls of the box is enough to produce the phase change, from gas to liquid.

As for the other options:

i) the gas molecules speed up due to collisions with the walls: No. As already stated the gas molecules slow down.

ii) the gas molecules vibrate around fixed positions: No, the gas molecules are not around fixed positions, they translate in right random motion.

iii) the gas molecules gain energy from the cold walls of the box: as already stated the gas molecules release energy which is transfered to the cold walls of the box.

8 0

3 years ago

A magnetic field is entering into a coil of wire with radius of 2(mm) and 200 turns. The direction of magnetic field makes an an

frozen [14]

Answer:

a) 2.278 x 10^-5 volts

b) 1.139 x 10^-6 Ampere

c) 2.59 x 10^-11 W

Explanation:

The radius of the wire r = 2 mm = 0.002 m

the number of turns N = 200 turns

direction of the magnetic field ∅ = 25°

magnetic field strength B = 0.02 T

varying time = 2 sec

The cross sectional area of the wire = $\pi r^{2}$

==> A = 3.142 x $0.002^{2}$ = 1.257 x 10^-5 m^2

Field flux Φ = BA cos ∅ = 0.02 x 1.257 x 10^-5 x cos 25°

==> Φ = 2.278 x 10^-7 Wb

The induced EMF is given as

E = NdΦ/dt

where dΦ/dt = (2.278 x 10^-7)/2 = 1.139 x 10^-7

E = 200 x 1.139 x 10^-7 = 2.278 x 10^-5 volts

b) If the two ends are connected to a resistor of 20 Ω, the current through the resistor is given as

$I$ = E/R

where R is the resistor

$I$ = (2.278 x 10^-5)/20 = 1.139 x 10^-6 Ampere

c) power delivered to the resistor is given as

P = $I$ E

P = (1.139 x 10^-6) x (2.278 x 10^-5) = 2.59 x 10^-11 W

4 0

3 years ago