Question

2.00 mol of a monatomic ideal gas (U = 1.5 nRT) is enclosed in an adiabatic, fixed vertical cylinder fitted with a smooth, light adiabatic piston. The piston is connected to a vertical spring of spring constant 200 N m^-1 as shown in figure. The area of cross  

section of the cylinder is 20.0 cm² . Initially, the spring is at 300 K. The atmospheric and the temperature of the gas is 300 K. the atmospheric pressure is 100 kPa. The gas is heated slowly for some time by means of an electric heater so as to move the piston up through 10 cm. Find (a) the work done by the gas (g) the final temperature of the gas and (c) the heat supplied by the heater.

Answer 1

 (a) The force by the gas on the piston is F = P₀ A + kx. Where P₀ = 100kPa is the atmospheric pressure, A = 20cm² is the area of cross section, k = 200 Nm⁻¹ is the spring constant and x is the compression of the spring. The work done by the gas as the piston moves through l = 10 cm is 

(b) The initial temperature is T₁ = 300 K. Let the final temperature be T₂ = 300 K. Let the final temperature be we have

(c) The internal energy is U = 1.5 nRT. The change in internal energy is ∆U = 1.5 nRT.