Question

2.8x10-2 kg of nitrogen is expanded isothermally
and reversibly at 300K from 15.15x105 Nm-2
when the work done is found to be -17.33 kJ.
Find the final pressure.
(1456.8 Nm-2).​

Answer 1

The final pressure is  $1456.8Nm^{-2}$

Step by step explanation:

From the given,

$w=-2.303\,nRTlog \frac{P_{1}}{P_{2}}$.....................(1)

Rearrange the equation is as follows.

$w=-2.303\times\,\frac{w}{m}RT\,log\,\frac{P_{1}}{P_{2}}$........................(2)

Work done = -17.33 kJ

Mass of nitrogen gas = 28 g/mol

Expanded weight of nitrogen = $2.8\times10^{-2}kg$

Substitute the values in equation (2)

$-17.33\,kg=-2.303\times \frac{2.8\times10^{2}10^{3}}{28}\times8.314\times300\,log\frac{15.15}{P_{2}}$

$=\frac{17.33\times 21\times10^{3}}{-2.303\times2.8\times10\times8.314\times300}=6.18-log_{10}^{P_{2}}$

$logp_{2}=6.18-3.017$

$logp_{2}=3.16$

$P_{2}=10^{3.163}$

$=1455.46\,N/m^{2}$

Therefore, final pressure is $=1455.46\,N/m^{2}$