2. A cylinder with a sliding piston contains an ideal gas. The cylinder (with th

Question

2. A cylinder with a sliding piston contains an ideal gas. The cylinder (with the gas inside) is heated by transferring the same amount of heat to the system by two different ways: c) The piston is blocked to prevent is from moving. d) The piston is allowed to slide frictionlessly to the end of the cylinder How does the final temperature of the gas under condit ion equal? temperature of the gas under condition 2? Is it possible for the temperatures to be nsi ion of an ideal gas takes place at 500 K and

Explanation / Answer

No it is not possible that both the temperatures be equal, with the same amount of heat being supplied. The situation in (c) is preventing any amount of work to be done on the piston to move it. The situation in (d) provides an option for some work to be done on the piston to move. If we take it completely frictionless then the volume is increasing so which means some work is done.

from the first law of thermodynamics

dQ=du+dW

here, du is the change in internal energy

dQ=cdT+pdV

where c is the specific heat. dV is the change in volume

for process (c) dQ=cdT (because dV=0)

for process (d) dQ=cdT+pdV

so in the second process, the final temperature will be lesser than the first. In the first process, the entire energy is spent on increasing the internal energy thereby raising its temperature.

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