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There are some missing data in the text of the exercise. Here the complete text:
"<span>A sample of 20.0 moles of a monatomic ideal gas (γ = 1.67) undergoes an adiabatic process. The initial pressure is 400kPa and the initial temperature is 450K. The final temperature of the gas is 320K. What is the final volume of the gas? Let the ideal-gas constant R = 8.314 J/(mol • K). "
Solution:
First, we can find the initial volume of the gas, by using the ideal gas law:
</span>
<span>where
p is the pressure
V the volume
n the number of moles
R the gas constant
T the absolute temperature
Using the initial data of the gas, we can find its initial volume:
</span>
<span>
Then the gas undergoes an adiabatic process. For an adiabatic transformation, the following relationship between volume and temperature can be used:
</span>
<span>where </span>
for a monoatomic gas as in this exercise. The previous relationship can be also written as
where i labels the initial conditions and f the final conditions. Re-arranging the equation and using the data of the problem, we can find the final volume of the gas:
![V_f = V_i \sqrt[\gamma-1]{ \frac{T_i}{T_f} }=(0.187 m^3) \sqrt[0.67]{ \frac{450 K}{320 K} }=0.310 m^3 = 310 L](https://tex.z-dn.net/?f=V_f%20%3D%20V_i%20%20%5Csqrt%5B%5Cgamma-1%5D%7B%20%5Cfrac%7BT_i%7D%7BT_f%7D%20%7D%3D%280.187%20m%5E3%29%20%5Csqrt%5B0.67%5D%7B%20%5Cfrac%7B450%20K%7D%7B320%20K%7D%20%7D%3D0.310%20m%5E3%20%3D%20310%20L%20%20)
So, the final volume of the gas is 310 L.
"<span>A sample of 20.0 moles of a monatomic ideal gas (γ = 1.67) undergoes an adiabatic process. The initial pressure is 400kPa and the initial temperature is 450K. The final temperature of the gas is 320K. What is the final volume of the gas? Let the ideal-gas constant R = 8.314 J/(mol • K). "
Solution:
First, we can find the initial volume of the gas, by using the ideal gas law:
</span>
<span>where
p is the pressure
V the volume
n the number of moles
R the gas constant
T the absolute temperature
Using the initial data of the gas, we can find its initial volume:
</span>
<span>
Then the gas undergoes an adiabatic process. For an adiabatic transformation, the following relationship between volume and temperature can be used:
</span>
<span>where </span>
where i labels the initial conditions and f the final conditions. Re-arranging the equation and using the data of the problem, we can find the final volume of the gas:
So, the final volume of the gas is 310 L.
Explanation:
A transformer consists of core of soft iron (a material that can be easily magnetized/demagnetized), to which two coils are attached at both ends.
An alternating current in the primary coil produces a magnetic field around the coil, magnetizing the iron core; therefore, the same magnetic field produces a magnetic flux in the secondary coil.
Since the AC current in the primary coil is variable, then the magnetic field also changes, so the magnetic flux through the secondary coil changes over time; therefore, an electromotive force (and so, a current) is induced in the secondary coil, according to Faraday-Newmann-Lenz:
where
is the induced emf
is the rate of change of magnetic flux through the secondary coil
We notice that this mechanism would not work if the current in the primary coil is a DC current: in fact, a DC current has always a constant value, so there is no change in the magnetic field, therefore no change in the magnetic flux through the secondary coil and no emf induced.