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Q53P

Expert-verifiedFound in: Page 1275

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**At what pressure, in atmospheres, would the number of molecules per unit volume in an ideal gas be equal to the number density of the conduction electrons in copper, with both gas and copper at temperature T =300K?**

The pressure value that would give the number of molecules per unit volume in an ideal gas equal to the number density of conduction electrons in copper is $3.49\times {10}^{3}\mathrm{atm}$.

a) The number of conduction electrons in copper,$n/V=8.43\times {10}^{28}{\mathrm{m}}^{-3}$

b) The temperature value, *T* =300 K

**The equation that relates the characteristic properties of an ideal gas is known as Ideal Gas Equation. The ideal gas equation can be given as-**

**PV=nkT**

Here *P* is the pressure,*V* is the volume, *n* id the number of moles and *k* is the Boltzmann constant.

Using the given condition and data in equation, we can get the value of the pressure in atmospheres as follows:

$P=\frac{nkT}{V}\phantom{\rule{0ex}{0ex}}=\left(8.43\times {10}^{28}{\mathrm{m}}^{-3}\right)\left(1.38\times {10}^{-23}\mathrm{J}/\mathrm{K}\right)\left(300\mathrm{K}\right)\phantom{\rule{0ex}{0ex}}=3.49\times {10}^{8}\mathrm{Pa}\phantom{\rule{0ex}{0ex}}=3.49\times {10}^{3}\mathrm{atm}$

Hence, the value of the pressure is $3.49\times {10}^{3}\mathrm{atm}$.

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