The internal energy of a monoatomic ideal gas is . One mole of helium is kept in a cylinder of cross — Thermodynamics and Thermochemistry Chemistry Question
Question
The internal energy of a monoatomic ideal gas is $1.5 nRT$. One mole of helium is kept in a cylinder of cross section $8.5\text{ cm}^2$. The cylinder is closed by a light frictionless piston. The gas is heated slowly in a process during which a total of 42 J heat is given to the gas. If the temperature rises through $2^\circ\text{C}$, find the distance moved by the piston (in cm). Atmospheric pressure = 100 kPa.
💡 Solution & Explanation
$\Delta U = 1.5 n R \Delta T = 1.5 \times 1 \times 8.314 \times 2 = 24.94\text{ J}$. From $q = \Delta U + W_{\text{exp}}$, expansion work $W_{\text{exp}} = 42 - 24.94 = 17.06\text{ J}$. $W_{\text{exp}} = P_{\text{ext}} \Delta V = P_{\text{ext}} \times A \times d$. $17.06 = (100 \times 10^3) \times (8.5 \times 10^{-4}) \times d \implies 17.06 = 85d \implies d \approx 0.2\text{ m} = 20\text{ cm}$. Format as 0020.