A) \[2\,R{{T}_{0}}\]
B) \[R{{T}_{0}}\]
C) \[\frac{3}{2}\,R{{T}_{0}}\]
D) \[\frac{1}{2}\,R{{T}_{0}}\]
Correct Answer: A
Solution :
In a process \[\operatorname{P}{{V}^{x}}=constant\], molar heat capacity is given by \[C=\frac{R}{\gamma -1}+\frac{R}{1-x}\] As the process is \[\frac{\operatorname{P}}{V}=constant\] i.e., \[P{{V}^{-1}}\] constant, therefore, \[\operatorname{x}= -1\]. For an ideal monatomic gas, \[\gamma =\frac{5}{3}\] \[\therefore \,\,\,\,C=\frac{R}{\frac{5}{3}-1}+\frac{R}{1-(-1)}=\frac{3}{2}R=2R\] \[\Delta Q=nC(\Delta T)=1(2\,R)\,(2{{T}_{0}}-{{T}_{0}})=2R{{T}_{0}}\]
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