The ratio of P to V at any instant is constant and is equal to 1. for a monoatomic ideal gas undergoing a process. What is the molar heat capacity of

Question

The ratio of P to V at any instant is constant and is equal to 1. for a monoatomic ideal gas undergoing a process. What is the molar heat capacity of

The ratio of P to V at any instant is constant and is equal to 1. for a monoatomic ideal gas undergoing a process. What is the molar heat capacity of the gas?
A. `(3R)/2`
B. `(4R)/2`
C. `(5R)/2`
D. `0`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - B
From first law of Thermodynamics , `DeltaE=q+w implies nC_vdT=nCdT-PdV` .. (1)
Now according to process , P=V and according to ideal gas equation , PV=nRT
We have , `V^2=nRT`
On differentiating , 2VdV=nRdT and PdV=VdV=`(nRdT)/2`
So from first equation we have, `nC_vdT=nCdT-(nRdT)/2`
So, `C_v=C-R/2` Hence C`=(4R)/2`