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Chemical: Gas-Related Problems

6. A gas operates under isothermal conditions. The initial volume of gas in the pump is 22.4 liters, the pressure is one atmosphere and temperature is 273 deg K. if 0.6 mole of gas is released and the volume remains unchanged calculate the new pressure.

7. Calculate the minimum energy a photon must have to produce an electron hole pair in an extrinsic semiconductor of band gap 1.3 electron volts.

8. A sealed flexible container of gas in good thermal contact with medium at 300 degree K is moved to another environment at 400 degree K. determine the percentage change in volume

9. With the container in the 400 degree K environment how much gas must be released to return the volume to value it had at 300 degree K.

10. The drift mobility of the free charge caries in a material is 10^-2 m^2 v^-1s^-1, the charge on the electron is 1.6*10^-19 coulombs. Calculate the density of free charge carries if the conductivity is 1.0*10^-6 ohm m.

Solution Preview

Please find the solution to your all the 5 question, from Q.6 to Q.10 in the attached word file 'Q6_10_Solution.doc'

6. A gas operates under isothermal conditions. The initial volume of gas in the pump is 22.4 liters, the pressure is one atmosphere and temperature is 273 deg K. if 0.6 mole of gas is released and the volume remains unchanged calculate the new pressure.

Answer:
Pressure = 1 atmosphere. and Temperature = 273 0K
These values of pressure and temperature are standard values and the gas is said to be at STP (i.e. Standard Temperature Pressure)

Standard volume of 1 mole of gas at STP = 22.4 litre.
When 0.6 mole of gas flows out, only 0.4 mole of the gas remains in the pump.

M1 = 1 mole of gas occupies the volume V1 = 22.4 liter volume.
∴ M2 = 0.4 mole of gas occupies the volume V2 liter.

Solve this by direct proportionality i.e. by linear equation.
∴ ---- (1)

The gas is released under isothermal conditions. The temperature 2730K remains constant throughout.

The change is isothermal. Use Boyle's law

Pressure x Volume = constant at const. temperature.
i.e. P1 x V1 = P2 x V2 = constant.

∴ New pressure P2 is given by
, using (1)
∴ Final pressure, P2 = 2.5 atmosphere.
-----------

7. Calculate the minimum energy a photon must have to produce an electron hole pair in an extrinsic semiconductor of band gap 1.3 electron volts.

Answer:
A photon can produce an electron-hole pair in a semiconductor only if it can excite the electron from valence band to conduction band, thus making it to cross the energy barrier.

Here the energy gap of the semiconductor Eg = 1.3 eV
i.e. Eg = 1.3 x 1.6 x 10-19 J
= 2.08 x 10-19 J

If a photon has the energy of 1.3 eV or 2.08 x 10-19 J, then it can excite the electron form the valence band to the conduction band, thus producing an electron-hole pair.

In ...

Solution Summary

This solution involves step-by-step calculations for gas-related problems.

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