One mole of an ideal diatomic gas is kept in a cylinder fitted with a frictionless piston. The piston area is 4 cm². The gas is heated slowly so that its temperature rises by 1.2°C, during which the piston moves outward by 25 mm. Atmospheric pressure is 100 kPa and R = 8.3 J·mol⁻¹·K⁻¹. Neglect the piston mass. Which listed value is the most suitable heat supplied ?
Options

Question

One mole of an ideal diatomic gas is kept in a cylinder fitted with a frictionless piston. The piston area is 4 cm². The gas is heated slowly so that its temperature rises by 1.2°C, during which the piston moves outward by 25 mm. Atmospheric pressure is 100 kPa and R = 8.3 J·mol⁻¹·K⁻¹. Neglect the piston mass. Which listed value is the most suitable heat supplied ?

Options

G1 Physics · Accepted Answer

from the first law using the stated piston displacement and the usual five active degrees of freedom for a diatomic ideal gas. For a diatomic ideal gas with translational and rotational degrees of freedom, f = 5, so Cᵥ = 5R ÷ 2. The change in internal energy is ΔU = nCᵥΔT = 1×(5R ÷ 2)×1.2. Using R = 8.3 J·mol⁻¹·K⁻¹: ΔU = 2.5×8.3×1.2 = 24.9 J. Now calculate the work from the stated piston displacement. Area: A = 4 cm² = 4×10⁻⁴ m². Displacement: x = 25 mm = 25×10⁻³ m. Therefore, ΔV = Ax = 4×10⁻⁴×…