Sm1 25thru1 26

PROBLEM 1.25 The FBD of a piston is as shown with a downward force due to the atmosphere (F_atm_ ) where F_atm_ = p_atm_ A_piston_ and A_piston_ is the cross sectional area of the piston. Another downward force is due to gravity (F_grav_ ) where F_grav_ = m_piston_ g and m_piston_ is the mass of the piston. The upward force (F_gas_ ) is due to the pressure exerted on the bottom face of the piston by the substance where F_gas_ = p_gas_ A_piston_ and p_gas_ is the pressure of the gas. Summing forces yields the following equation that can be rearranged to explore whether p_gas_ is constant. It is assumed that up is positive. F_gas_ = F_grav_ + F_atm_ F_gas_ = p_gas_ A_piston_ A_piston_ p_gas_ A_piston_ = m_piston_ g + p_atm_ A_piston_ m_piston_ g p_gas_ = + p_atm_ A_piston_ Since each of the four quantities on the right-side of the above equation is constant, it follows that the pressure acting on the bottom of the piston remains constant. Volume change occurs as the gas is heated or cooled. PROBLEM 1.26 Since the piston moves smoothly within the cylinder, the piston begins to rise when the force exerted by the gas exceeds the resisting force composed of the piston weight and the force exerted by the atmospheric pressure. That is, F_gas_ > Weight + F_atm_ p_gas_ A > mg + p_atm_ A m g p_gas_ > + p_atm_ p_gas_ > 50kg (9.81m/s^2_ )1 bar 1N_ |01 > + 1 bar 1.49 bar