A) 3
B) \[\frac{5}{2}\]
C) \[\frac{5}{3}\]
D) None of these
Correct Answer: B
Solution :
V-T graph is a straight line passing through origin. Hence, \[\operatorname{V}\propto T\,\,or\,\,P =constant\] \[\therefore \,\,\,\,\Delta Q=\,{{\,}_{n}}{{C}_{P}}\Delta U\,\,=\,{{\,}_{n}}{{C}_{V}}\Delta T\] Also \[\Delta W=\Delta Q-\Delta U=\mu ({{C}_{P}}-{{C}_{V}})\Delta T\] \[\therefore \,\,\,\frac{\Delta Q}{\Delta W}\,\,=\,\,\frac{n{{C}_{P}}\Delta T}{n({{C}_{P}}-{{C}_{V}})\Delta T}\,\] \[=\,\,\,\frac{{{C}_{P}}}{{{C}_{P}}-{{C}_{V}}}\,\,=\,\,\frac{1}{1-\frac{{{C}_{V}}}{{{C}_{P}}}}\] \[\frac{{{C}_{V}}}{{{C}_{P}}}\,\,=\,\,\frac{3}{5}\,\,\,for\,\,helium\,\,gas.\] Hence \[\frac{\Delta Q}{\Delta W}=\,\,\frac{1}{1-3/5}=\frac{5}{2}\]
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