Question

The molar specific heat of the process $V\propto T^4$ for ${CH}_4$ gas at room temperature is:

• A. 4R
• B. 7R
• C. 3R
• D. 8R

Answer 1

The correct option is D 8R

$\begin{array}{c}V{T}^{-4}=cons\tan t\\ V.{\left(PV\right)}^{-4}=cons\tan t\\ P^{-4}{V}^{-3}=cons\tan t\\ P{V}^{{}^{3/4}}=cons\tan t\\ w=\frac{nR\Delta T}{1-\frac{3}{4}}=4nRT\\ u=\frac{1}{2}nR\Delta T\\ \Delta Q=n\left(\frac{1}{2}+4\right)R\Delta T\\ \therefore C=\left(\frac{1}{2}+4\right)R\\ \therefore f=8\\ \therefore C=8R\\ Hence,\\ optionDiscorrectanswer.\end{array}$