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Found in: Page 1275

### Fundamentals Of Physics

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 $3.49×{10}^{3}\mathrm{atm}$.

See the step by step solution

## Step 1: The given data

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

b) The temperature value, T =300 K

## Step 2: Understanding the concept of ideal gas equation

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.

## Step 3: Calculation of the pressure

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

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

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