question_answer

Show that the product of pressure and volume has the dimensions of energy. Derive the value for 1 litre-atmosphere.

Answer:

                \[P\times V=\frac{\text{Force}}{\text{Area}}\times \text{Volume}=\frac{\text{Force}\,\times {{\text{(Length)}}^{\text{3}}}}{{{\text{(Length)}}^{\text{2}}}}=\]             \[\text{Force}\times \text{Length}=\text{work}\], which has same units as that of energy. 1 L atm = (1 \[d{{m}^{3}}\]) (101325 N \[{{m}^{-2}}\]) = (\[{{10}^{-3}}{{m}^{3}}\]) (101325 N \[{{m}^{-2}}\]) = 101.325 N m = 101.325 J.