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Consider all possible isothermal contractions of an ideal gas. The change in ent

ID: 1961137 • Letter: C

Question

Consider all possible isothermal contractions of an ideal gas. The change in entropy of the gas:
increases for all of them
does not decrease for any of them
is zero for all of them
does not increase for any of them
decreases for all of them

Consider the following processes: The temperature of two identical gases are increased from the same initial temperature to the same final temperature. Reversible processes are used. For gas A the process is carried out at constant volume while for gas B it is carried out at constant pressure. The change in entropy:
is greater for B
is the same for A and B
is greater for A only if the initial temperature is high
is greater for A
is greater for A only if the initial temperature is low

Explanation / Answer

The change in entropy of an isothermal process is always

                        ( S ) T =  nR ln ( V2 / V1 )

For any process, the change entropy is always increases.
The change in entropy of an isothermal process is always
increases for all of them.
------------------------------------------------------------------------------------------------- The change in entropy of a gas A ( which takes place at constant volume)               ( S ) v = Cv ln ( T2 / T1 )     ....... (1) Here,   T1 and     T2      are inital and final temperature of the process The specific heat at constant volume is Cv The change in entropy of a gas  B ( which takes place at constant pressure )             ( S )p = Cp ln ( T2 / T1 )    ....... (2)      
The specific heat at constant pressure is Cp
From equations   (1) and (2), Since, Cp > Cv
                    ( S )p >   ( S ) v
The change in entropy is greater for B The change in entropy of a gas  B ( which takes place at constant pressure )             ( S )p = Cp ln ( T2 / T1 )    ....... (2)      
The specific heat at constant pressure is Cp
From equations   (1) and (2), Since, Cp > Cv
                    ( S )p >   ( S ) v
The change in entropy is greater for B From equations   (1) and (2), Since, Cp > Cv
                    ( S )p >   ( S ) v
The change in entropy is greater for B
                    ( S )p >   ( S ) v
The change in entropy is greater for B The change in entropy is greater for B