Two adiabatic processes involving a given amount of an ideal gas are plotted on a P-V diagram. A, B, C and D are four points on these curves as shown in the diagram. AC is the line parallel to pressure axis where as the volume at B is just smaller and at D is just more than that of volume at A by same fraction. Which of the following statements are true?

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Heat is given to the system in the process AD and is lesser than the magnitude of heat involved in the process AC.

Heat is given to system in the process AB and rejected by the system in the process AD but both the magnitudes are same.

Heat is given to the system in the process AB and is greater than the magnitude of heat involved in the process AD.

Heat is rejected by the system in the process AD and is lesser than the magnitude of heat involved in the process AC.

answer is B, C.

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Detailed Solution

$d Q_{A C} + d Q_{B A} = - v e d Q_{A C} - d Q_{A B} = - v e d Q_{A C} = - v e - x | d Q_{A C} | = somevalue + x$

Similarly we can show $d Q_{A D}$ is less in magnitude

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