The constant volume heat capacity of a gas can be measured by observing the decrease in temperature when it expands adiabatically and reversibly. If the decrease in pressure is also measured, we can use it to infer the value of γ = Cp/Cv and hence, by combining the two values, deduce the constant-pressure heat capacity. A fluorocarbon gas was allowed to expand reversibly and adiabatically to twice its volume; as a result, the temperature fell from 298.15 K to 248.44 K and its pressure fell from 202.94 kPa to 81.840 kPa. Evaluate Cp

The value is  

Explanation:

From the question we are told that  

The  initial volume of the  fluorocarbon gas is  

 The final  volume of the fluorocarbon gas is

  The initial  temperature of the fluorocarbon gas is  

  The final  temperature of the fluorocarbon gas is

   The initial  pressure is

    The final   pressure is  

Generally the equation for  adiabatically reversible expansion is mathematically represented as

Here R is the ideal gas constant with the value  

So  

=>

Generally adiabatic reversible expansion can also be mathematically expressed as

=>    

=>  

=>    

So

=>