Consider a cylinder of gas that is kept at constant temperature and whose volume can be changed by moving a piston. Suppose that, initially, the container holds 2 moles of gas at a pressure of 100 kPa and a temperature of 300 K. With the temperature held constant, the pressure is raised to 101 kPa, producing a change in volume. By calculating the change in volume, determine the bulk modulus for this gas, under these conditions. A) 1.01 × 10⁵ N/m² B) 2.02 × 10⁵ N/m² C) 1.01 × 10⁴ N/m² D) 2.02 × 10⁴ N/m² E) 2.02 × 10⁶ N/m²

Question

Quizplus · Accepted Answer

The bulk modulus is given by B = -V * (ΔP/ΔV). Using the ideal gas law, PV = nRT, and knowing that temperature and moles are constant, we find ΔV. The initial volume V1 = nRT/P1 = (2 * 8.314 * 300) / 100,000 = 0.049884 m³. The final volume V2 = nRT/P2 = (2 * 8.314 * 300) / 101,000 = 0.049385 m³. ΔV = V2 - V1 = -0.000499 m³. ΔP = 101,000 - 100,000 = 1,000 Pa. B = -V1 * (ΔP/ΔV) = 0.049884 * (1,000 / -0.000499) = 1.01 × 10⁵ N/m².

Consider a Cylinder of Gas That Is Kept at Constant