The specific heat of a gas one measured as CP=12.28±0.2) units and Cv=3.97±0.3) units find the value of percentage error of real gas constant 'R'

Universal Gas constant R=Cp−Cv percentage error in R=ΔCp+ΔCvCp−Cv×100 here R=Cp−Cv R=12.28−3.97=8.31 Unitspercentage error in R is ΔRR×100=ΔCp+ΔCvCp−Cv×100 ΔRR×100=0.2+0.38.31×100 ΔRR×100=6.016%=percentage error in R

The specific heat of a gas one measured as CP=12.28±0.2) units and Cv=3.97±0.3) units find the value of percentage error of real gas constant 'R'

Universal Gas constant R=Cp−Cv percentage error in R=ΔCp+ΔCvCp−Cv×100 here R=Cp−Cv R=12.28−3.97=8.31 Unitspercentage error in R is ΔRR×100=ΔCp+ΔCvCp−Cv×100 ΔRR×100=0.2+0.38.31×100 ΔRR×100=6.016%=percentage error in R

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The specific heat of a gas one measured as $C_{P} = 12.28 \pm 0.2)$ units and $C_{v} = 3.97 \pm 0.3)$ units find the value of percentage error of real gas constant $' R'$

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5.015%

6.016%

8.018%

4.014%

answer is B.

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Detailed Solution

$U n i v e r s a l G a s c o n s \tan t R = C_{p} - C_{v} p e r c e n t a g e e r r o r i n R = \frac{Δ C_{p} + Δ C_{v}}{C_{p} - C_{v}} \times 100$

$h e r e R = C_{p} - C_{v} R = 12.28 - 3.97 = 8.31 U n i t s$

$p e r c e n t a g e e r r o r i n R i s \frac{Δ R}{R} \times 100 = \frac{Δ C_{p} + Δ C_{v}}{C_{p} - C_{v}} \times 100 \frac{Δ R}{R} \times 100 = \frac{0.2 + 0.3}{8.31} \times 100 \frac{Δ R}{R} \times 100 = 6.016 % = p e r c e n t a g e e r r o r i n R$