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

Question

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 (A) 4.16J/cal (B) 4.18J/cal (C) 4.20J/cal (D) 4.22 J/cal

Tardigrade Admin · Accepted Answer

We know that Cp-Cv=(R/J) ⇒ J=(R/Cp-Cv) Cp-Cv=1.98(cal/g-mol-K) R=8.32(J/g-mol-K) J=(8.32/1.98)=4.20J/cal

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

4.16J/cal

4.18J/cal

4.20J/cal

4.22 J/cal

We know that $C_{p} - C_{v} = \frac{R}{J}$ $\Rightarrow$ $J = \frac{R}{C _{p} - C _{v}}$ $C_{p} - C_{v} = 1.98 \frac{c a l}{g - m o l - K}$ $R = 8.32 \frac{J}{g - m o l - K}$ $J = \frac{8.32}{1.98} = 4.20 J / c a l$

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 Cp​ and Cv​ of the gas is 1.98 cal/g mol-K. From this data value of J is