The molar heat capacity of a gas in a process

Options

A. is either `C_(V) or C_(P)`
B. lies between `C_(V) or C_(P)`
C. may range from zero to infinity
D. can have any real value

Answer

D

Explanation

Since `DeltaQ = DeltaU +DeltaW`, from first law of thermodymics,
`:.` The molar heat capacity `C` is given by
`C = (DeltaQ)/(nDeltaT) = (DeltaU+DeltaW)/(nDeltaT)`
Assuming `DeltaT` to be positive `C gt = lt 0`, accordingly as `DeltaU gt = lt -DeltaW`
`i.e. `C` can be positive zero or negative.
Further as `DeltaT gt rarr 0, C rarr +-oo`
ans `DeltaT rarr oo, C rarr 0`
In other words, `C` can have any real value, depending upon the type of thermdymic process.