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                This question has statement -1 and statement -2. Of the four choices given after the Statements, choose the one that best describes the two Statements.                 Statement-1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.                 Statement 1: A perfect gas is heated keeping pressure constant pressure is lower than that at constant volume.     JEE Main Online Paper ( Held On 23  April 2013 )

A)   Statement-1 is true, Statement-2 is true, and Statement 2 is the count explanation of Statement 1.

B)                                          Statement -1 is true, Statement-2 is false.

C)                                          Statement 1 is true, Statement 2 is true but Statement 2 is not the correct explanation of Statement 1.

D)                                          Statement -1 is false, Statement -2 is true.

Correct Answer: C

Solution :

                  Internal energy of a system is the energy possessed by the system due to molecular motion and molecular configuration. Internal energy \[u={{u}_{k}}+{{u}_{p}}\] For an ideal gas there is no molecular attraction \[{{u}_{p}}=0\] \[\therefore \]Internal energy\[u={{u}_{k}}\](i.e., internal kinetic energy)  and \[u={{u}_{k}}=\frac{3}{2}\mu RT\] At constant pressure \[{{(\Delta Q)}_{P}}=\mu {{C}_{p}}\Delta T\] At constant volume  As\[{{C}_{P}}>{{C}_{v}}\therefore {{(\Delta T)}_{P}}<{{(\Delta T)}_{v}}\]