The specific heats of a gas are measured as Cₚ = (12.28 ± 0.2) units and Cv=(3.97 ± 0.3) units. Find the value of real gas constant R and percentage error in R.

The correct option is 6.016%.

Let us find the value of the gas constant R and the percentage error in it step-by-step.

Step 1: Calculate the value of the gas constant R
The relation between the specific heat at constant pressure (C_p), the specific heat at constant volume (C_v), and the gas constant (R) is given by Mayer's formula:

$R=C_p-C_v$

Given:

$C_p=12.28$

units and

$C_v=3.97$

units. Substituting these values, we get:

$R=12.28-3.97=8.31$

units.

Step 2: Calculate the absolute error in the gas constant (ΔR)
When two quantities are subtracted, their absolute errors are added together to find the absolute error in the final result:

$\Delta R=\Delta C_p+\Delta C_v$

Given the measured errors:

$\Delta C_p=0.2$

units and

$\Delta C_v=0.3$

units. Thus, the absolute error in R is:

$\Delta R=0.2+0.3=0.5$

units.

Step 3: Calculate the percentage error in R
The percentage error in R is given by the formula:

$\text{Percentage Error}=\frac{\Delta R}{R}\times 100\%$

Substituting the calculated values of R and ΔR:

$\text{Percentage Error}=\frac{0.5}{8.31}\times 100\%$

$\text{Percentage Error}=\frac{50}{8.31}\%\approx 6.0168\%\approx 6.016\%$

Therefore, the percentage error in R is approximately 6.016%.