Consider a horizontal cylinder-and-piston device similar to the one shown in Fig

Question

Consider a horizontal cylinder-and-piston device similar to the one shown in Fig 3.4 on page 70. The piston has mass m The cylinder wall is diathermal. and to in thermal contact with a heat reservoir of temperature T_ext The system is an amount n of an ideal gas confined in the cylinder by the piston. The initial state of the system is an equilibrium stale described by p_1 and T =T_ext There is a constant external pressure pw. equal to twice p_1 that supplies a constant external force on the piston When the piston is released, it begins to move to the left to compress the gas. Make the idealized assumptions that the piston moves with negligible friction; and the gas remains practically uniform (because the piston is massive and its motion is slow) and has a practically constant temperature T = T_ext, Describe the resulting process. Describe how you could calculate w and q during the period needed for the piston velocity to become zero again. Calculate w and q during this period for0.500 mol gas at 300k

Explanation / Answer

a) the temperature is constant so the system is isothermal

b) There is no change in temperature so the change in internal energy = 0

Also Heat = work done

the work done will be positive as the gas is being compressed

Work done = work initial - workfinal = nRT ln (Vf / Vi)

Now the external pressure = 2X internal pressure

And volume is inversely proportional to pressure

So the final volume = half of intial volume

n = moles = 0.5

R = 8.314

T = 300K

c) work done = 0.5 X 8.314 X 300 ln (ln(1/2) = 864.24 Joules

Heat = -864.24 Joules

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