Question

A cylinder contains a certain amount of He gas, see Figure. The total mass of the piston and the extra weight is m, the mass of He is negligible in comparison The area of the piston is A. The atmospherio pressure outside the cylinder is zero but gravity plays its role, acceleration of gravity being g Initially the gas is in an equilibrium state with volume V0​ and temperature T0​. The cylinder is then placed in thermal contact with a very large body of temperature 2T0​ and gradually (because the thermal contact is not strong) reaches a new final equilibrium state.

a) Show the process, from the initial to the final state, in the PV diagram In the following express your answers in terms of the data given

Answer 1

The process described involves a cylinder with helium gas undergoing a temperature change, reflecting an isothermal process on a PV diagram as a hyperbolic curve. The work done by the gas is equivalent to the heat added as it expands in response to a temperature rise, and this can be calculated using the ideal gas law.

Step-by-step explanation:

The student's question is rooted in the principles of thermodynamics, specific to the behavior of an ideal gas during thermodynamic processes within a piston-cylinder assembly. The process described involves a cylinder with helium gas undergoing a temperature change from T0 to 2T0, which will affect its volume and pressure according to the ideal gas law and principles of thermodynamics. Initially, in equilibrium, the gas has volume V0 and temperature T0. When in thermal contact with a body at temperature 2T0, it reaches a new equilibrium state at the same temperature. The isothermal process at temperature 2T0 can be graphically represented on a PV diagram (pressure-volume plot) as a hyperbolic curve since the pressure inversely varies with volume.

During this process, no heat is lost to the surroundings, and the total internal energy remains constant. As a result, the work done by the gas during expansion is equal to the heat added to the system. The change in volume from V0 to the final volume can be calculated using the ideal gas law, which in turn allows for the determination of the work done by the gas during the process.