A) \[\int\limits_{{{U}_{1}}}^{{{U}_{2}}}{dU}={{U}_{2}}-{{U}_{1}}\]
B) \[\int\limits_{{{w}_{1}}}^{{{w}_{2}}}{dU}\ne {{w}_{2}}-{{w}_{1}}\]
C) \[{{P}_{(adiabatic\,\,expansion)}}<{{P}_{(isothermal\,\,expansion)}}\]
D) \[{{V}_{(adiabatic\,\,expansion)}}>{{V}_{(isothermal\,\,expansion)}}\]
Correct Answer: D
Solution :
[d] Statement (1) is CORRECT: U(internal energy) is a state function and differential of energy, du is an exact diffrential. (P, V, T and U are state function). Statement (2) is CORRECT: Work (w) is not a state function, (depends on path). Thus differential of heat and work (eg., dq and dw) respectively are inexact differentials. Statement (3) is CORRECT: \[{{P}_{adia}}<{{P}_{iso}}\]. Since in adiabatic expansion, there is a fall of temperature, hence according to Charle's law (\[P\propto T\]at constant V and m). There is a corresponding fall of pressure so that \[{{P}_{adia}}<{{P}_{iso}}\] Statement (4) is INCORRECT Since in adiabatic expansion, there is a fall of temperature, hence according to Charle's law (\[P\propto T\]at constant ^and m), there is a corresponding decrease in volume, so that \[{{V}_{adia}}<{{V}_{iso}}\]. as expected \[{{W}_{iso}}\]. expansion \[>{{W}_{adia}}\] expansion.
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