Chemistry: Molecular Approach (4th Edition)

Published by Pearson
ISBN 10: 0134112830
ISBN 13: 978-0-13411-283-1

Chapter 1 - Exercises - Page 41: 137


\[\begin{align} & 1\text{ J}=1\text{ kg }{{\text{m}}^{\text{2}}}\text{/}{{\text{s}}^{\text{2}}} \\ & \text{m}\,\,\text{=}\,\,\text{kg,}\,\,{{\text{v}}^{\text{2}}}\,=\,{{\left( \text{m/s} \right)}^{2}},\text{thus,mv}\,\,\text{=}\,\,\text{kg}\,{{\text{m}}^{\text{2}}}\,{{\text{s}}^{\text{2}}} \\ & \text{P}\,\,\text{=}\,\,\text{N/}{{\text{m}}^{2}}\,=\,\,\text{kg}\,\,\text{m/}{{\text{s}}^{\text{2}}}\text{/}{{\text{m}}^{\text{2}}}\,=\,\,\text{kg/m}\ {{\text{s}}^{{}}} \\ & \text{V}\,\,\text{=}\,\,{{\text{m}}^{3}}\,,\,\text{PV}\,\,=\,\text{kg}\,\,{{\text{m}}^{3}}/\text{m}{{\text{s}}^{2}}\,\,=\,\,\text{kg}\,{{\text{m}}^{\text{2}}}\text{/}{{\text{s}}^{\text{2}}} \\ \end{align}\]

Work Step by Step

The SI unit of energy is Joule (J). \[1\text{ J}=1\text{ kg }{{\text{m}}^{\text{2}}}\text{/}{{\text{s}}^{\text{2}}}\] Now, \[E=\frac{1}{2}m{{v}^{2}}\]. The SI unit of mass is kilogram and velocity is \[\text{m/s}\]. Thus, \[\begin{align} & \frac{1}{2}m{{v}^{2}}=\text{kg }{{\left( \text{m/s} \right)}^{2}} \\ & =\text{kg }{{\text{m}}^{\text{2}}}\text{/}{{\text{s}}^{\text{2}}} \end{align}\] The SI unit of pressure is calculated as follows: \[\begin{align} & P=\frac{F}{A} \\ & =\frac{ma}{A} \end{align}\] The SI unit of mass is kg, acceleration is \[\text{m/}{{\text{s}}^{\text{2}}}\], and area is \[{{\text{m}}^{2}}\]. Thus, \[\begin{align} & \frac{ma}{A}=\frac{\text{kg}\left( \text{m/}{{\text{s}}^{2}} \right)}{{{\text{m}}^{2}}} \\ & =\text{kg/(m }{{\text{s}}^{2}}) \end{align}\] Similarly, \[E=\frac{3}{2}PV\]. The SI unit of pressure is \[\text{kg/(m}\ {{\text{s}}^{\text{2}}})\] and volume is \[{{\text{m}}^{3}}\]. Thus, \[\begin{align} & \frac{3}{2}PV=\left( \text{kg/(m}\ {{\text{s}}^{2}}) \right)\left( {{\text{m}}^{\text{3}}} \right) \\ & =\text{kg }{{\text{m}}^{\text{2}}}\text{/}{{\text{s}}^{\text{2}}} \end{align}\] The derived SI units of both these terms are those of energy.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.