1. Tardigrade
  2. Question
  3. Physics
  4. During an experiment, an ideal gas is found to obey an additional law VP2= constant. The gas is initially at a temperature T, and volume V. When it expands to a volume 2V, the temperature becomes:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. During an experiment, an ideal gas is found to obey an additional law $ V{{P}^{2}}= $ constant. The gas is initially at a temperature T, and volume V. When it expands to a volume 2V, the temperature becomes:

JIPMERJIPMER 2002Thermal Properties of Matter

Solution:

For an ideal gas, the relation is $ PV=RT $ ?(i) Given $ V{{P}^{2}}=K $ ?(ii) Squaring equation (i) we get $ {{P}^{2}}{{V}^{2}}={{R}^{2}}{{T}^{2}} $ ?(iii) Now dividing equation (ii) by (iii) $ \frac{1}{V}=\frac{K}{{{R}^{2}}{{T}^{2}}} $ If volume V expands to volume 2V so $ {{T}^{2}}\propto V $ Hence $ \frac{T_{1}^{2}}{T_{2}^{2}}=\frac{V}{2V}=\frac{1}{2} $ so, $ {{T}_{2}}=\sqrt{2}\,{{T}_{1}} $