Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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During an Experiment, an Ideal Gas is Found to Obey an Additional Law Pv2 = Constant. the Gas is Initially at a Temperature T and Volume V. Find the Temperature When It Expands to a Volume 2v. - Physics

Sum

During an experiment, an ideal gas is found to obey an additional law pV2 = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.

Use R = 8.3 J K-1 mol-1

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Solution

Applying equation of state of an ideal gas, we get
PV = nRT
⇒ P = \[\frac{nRT}{V}  . . . 1 \]
Taking differentials, we get
⇒ PdV + VdP = nRdT  . . . 2
Applying the additional law, we get
PV2 = c
V2 dP + 2VPdV = 0
⇒ VdP + 2PdV = 0  . . . 3
Subtracting eq. (3) from eq. (2) , we get
 PdV = -nRdT
⇒ dV = \[\ {-}\frac{nR}{P}dT \]
Now ,
⇒ dV = \[\ {-}\frac{V}{T}dT \]  [From  eq. (1}]
⇒ \[\frac{dV}{V} = {-}\frac{dT}{T} \] 
Integrating between T2 and T1 , we get
⇒ \[\int\limits_{V_1}^{2V} = {-}\int\limits_{T_1}^{T_2}\]
⇒  ln( 2V) - ln(V) = ln (T1) - ln (T2
⇒ `ln ((2V)/V)` = `ln ((T_1)/(T_2))`
⇒ `T_2 = T_1/2`

Concept: Kinetic Theory of Gases and Radiation - Kinetic Interpretation of Temperature
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 2 Kinetic Theory of Gases
Q 28 | Page 35
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