A certain quantity of ideal gas takes up `56J` of heat in the process AB and 360 J in the process AC. What is the number of degrees of freedom of the gas.

Explanation

`DeltaQ_(AB)=nC_(p)DeltaT=(gamma)/(gamma-1)nRDeltaT`
`=(gamma)/(gamma-1)[3P_(0)V_(0)-P_(0)V_(0)]=2PV_(0)xx(gamma)/(gamma-1)`
`DeltaQ_(AC)=DeltaU+Deltaw`
`=(nR)/(gamma-1)DeltaT+(1)/(2)xx3V_(0)[P_(0)+4P_(0)]`
`=([16P_(0)V_(0)-P_(0)V_(0)])/(gamma-1)+(15P_(0)V_(0))/(2)`
`56=2P_(0)V_(0)xx(gamma)/(gamma-1)` ,brgt `360=15P_(0)V_(0)[(gamma+1)/(2(gamma-1))]`
`(360)/(56)=(15)/(4)((gamma+1))/(gamma)`
`12gamma=7gamma+7`
`gamma=(7)/(5)=1+(2)/(f)impliesf=5`