A cylinder with a movable piston contains a gas. Initially the gas temperature i

Question

A cylinder with a movable piston contains a gas.  Initially the gas temperature is 25 degrees C.  A two stage process happens.  In stage 1, the cylinder is placed in boiling water.  With the piston held fixed, 2,000 calories of heat transfer from the boiling water to the gas raising it to 100 degrees C.  In stage 2, the piston is allowed to move.  The piston rises to a new position doing 100 J of work on its surrounds and again equilibrates at 100 degrees C.  Calculate (in Joules) DU for stage 1 and Q for stage 2.  

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Explanation / Answer

T1 = 25 deg clesius = 298 k

Stage -1

Constant volume process

T2 = 100 deg celsius = 373 k

work done on gas = dQ= 2000 cal = 8368 KJ

dU = dQ - PdV

dV=0

therefore dU = dQ

==> dU = 2000cal = 8368 K

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