First slide

Accuracy; precision of instruments and errors in measurements

Question

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 $' R'$

Moderate

A

5.015%
B

6.016%
C

8.018%
D

4.014%

Solution

$U n i v e r s a l G a s c o n s \tan t R = C_{p} - C_{v} p e r c e n t a g e e r r o r i n R = \frac{Δ C_{p} + Δ C_{v}}{C_{p} - C_{v}} \times 100$
$h e r e R = C_{p} - C_{v} R = 12.28 - 3.97 = 8.31 U n i t s$
$p e r c e n t a g e e r r o r i n R i s \frac{Δ R}{R} \times 100 = \frac{Δ C_{p} + Δ C_{v}}{C_{p} - C_{v}} \times 100 \frac{Δ R}{R} \times 100 = \frac{0.2 + 0.3}{8.31} \times 100 \frac{Δ R}{R} \times 100 = 6.016 % = p e r c e n t a g e e r r o r i n R$

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