1. Tardigrade
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  4. The value of the gas constant (R) calculated from the perfect gas equation is 8.32 J/g mol-K, whereas its value calculated from the knowledge of Cp and Cv of the gas is 1.98 cal/g mol-K. From this data value of J is

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Q. The value of the gas constant (R) calculated from the perfect gas equation is 8.32 J/g mol-K, whereas its value calculated from the knowledge of $ {{C}_{p}} $ and $ {{C}_{v}} $ of the gas is 1.98 cal/g mol-K. From this data value of J is

MGIMS WardhaMGIMS Wardha 2008

Solution:

We know that $ {{C}_{p}}-{{C}_{v}}=\frac{R}{J} $ $ \Rightarrow $ $ J=\frac{R}{{{C}_{p}}-{{C}_{v}}} $ $ {{C}_{p}}-{{C}_{v}}=1.98\frac{cal}{g-mol-K} $ $ R=8.32\frac{J}{g-mol-K} $ $ J=\frac{8.32}{1.98}=4.20J/cal $