The first law of thermodynamics was given as `q=DeltaU+(-w)`, where `q` is heat given to a system and `DeltaU` represents increase in internal energy and `-w` is work done by the system. Various processes such as isothermal, adiabatic, cyclic, isobaric and isochoric process in terms of `I` law of thermodynamics leads for important results. The molar heat capacity for `1` mole of monoatomic gas is `3/2 R` at constant volume and `5/2 R` at constant pressure.
`1` mole of a monoatomic gas is expanded through path `ABC` as shown in figure:
select the correct statements:

Options

A. If specific heat of gas are `0.125` and `0.075 cal//g` the mol. Wt of gas `=40`
B. Temperature at point `A,B,C` are `273,546` and `273 K` respectively.
C. Both `A` and `B`
D. None of these

Answer

a

Explanation

`C_(p)-C_(v)=R/M`
`:. 0.125-0.075=2/M`
`:. M=40`
At`A,P=1 atm, V=22.4 L`
At `B,T=1atm, V=44.8 L`
`:. T=546 K`
At `C,P=0.5atm, V=44.8 L`
`:. T=273 K`
Also `DeltaU=PxxDeltaV`
`=1xx22.4 L atm`
`=(1xx22.4)/0.0821xx8.314 J`
`=2268.37 J`
`=2.27 k J`
At constant `V, DeltaU=C_(v)xxDeltaT`
`=0.075xx40xx4.12xx273`
`=3.44 k J`