Two identical containers of the same amount and type of ideal gas follow differe

Question

Two identical containers of the same amount and type of ideal gas follow different processes from state A to state B, as shown in the PV diagram to the right. You are told that for one of the two processes heat is transferred into the gas, while for the other heat is transferred out. Consider the following statements and select a conclusion.

I: Heat is transferred into the gas in process #1.

II: The gas is at a higher temperature in state A.

a. I is true, II is false.

b. II is true, I is false.

c. Both I and II are true.

d. Both I and II are false.

e. One of those statements is true and the other is false, but there is not enough information to determine which is which.

Explanation / Answer

as we know, according to thermodynamics first law

heat given to system = work done by system + change in internal energy

now for both systems, initial and final values of P,V are same so temperature must be same. so change in internal energy for both is same.

now volume is decresing for both so work is done on system so work done is -ve

now if say second statement is true then temperature decreses so chnage in internal energy is also -ve so heat given to system is also -ve thus heat is given by system so first statement is false

so both statement are contradictory

so option e is correct

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