As illustrated in the figure, a cylindrical container holds oxygen ( = 1.4 ) and is sealed by a 50 kg frictionless piston. The cross-sectional area is 100 cm ^2 , the atmospheric pressure is 100 kPa , and g is 10 m s ⁻² . The cylinder is slowly heated for a period of time. Determine the amount of heat supplied to the gas if the piston is displaced outward by a distance of 20 cm .

Step-by-step solution

The pressure of the gas inside the cylinder is the sum of the atmospheric pressure and the pressure due to the weight of the piston. P = P_ atm + mg A Substituting the given values: P = 100 10^3 + 50 10 100 10⁻⁴ P = 10^5 + 0.5 10^5 = 1.5 10^5 Pa Since the cylinder is heated slowly, the process is isobaric. The change in volume of the gas is: V = A d = 100 10⁻⁴ 0.2 = 2 10⁻³ m ^3 The work done by the gas during this expansion is: W = P V = (1.5 10^5) (2 10⁻³) = 300 J For an isobaric process, the heat supplied Q is re