A monatomic ideal gas is following the cyclic proces ABCA. Then choose

1.	A monatomic ideal gas is following the cyclic proces ABCA. Then choose the incorrect option.
Answer» molar heat capacity for the process AB is `R/2` Heat is rejected by the system in path BC. Molar heat capacity for the process BC is `(2)/(3)R` Work done by the system in the process CA is `(2U_(0))/(3)ln4` Solution :For path AB TV = constant `RARR PV^(2)`=constant For polytropic process `PV^(m)`=constant On comparing eqn (i) and (ii) m=2 The molar heat capacity is GEVEN as `C=(R )/(GAMMA-1)-(R )/(m-1)`, for monatiomic `gamma=(5)/(3)` `C=(3R)/(2)-R=(R)/(2)` `C=((R/5)/(3)-1)-(R )/(2-1)=(3)/(2)R-R=(R )/(2)` so option (a) is correct . For BC it is an isochoric process and temperature is decreaseing so option (b) is correct. `C=C_(V)=(3)/(2)R`, so option (c )is wrong. For process CA (isothermal) `W=nRTln(V_(A)/(V_(C )))` `W=(2)/(3)/(2)nRT)ln(4)` `=(2)/(3)U_(0)ln(4)` So, option (d) is correct.

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