Question
A gas can be taken from $$A$$ to $$B$$ via two different processes $$ACB$$ and $$ADB.$$
A gas can be taken from $$A$$ to $$B$$ via two different processes $$ACB$$ and $$ADB.$$
When path $$ACB$$ is used 60$$J$$ of heat flows into the system and 30 $$J$$ of work is done by the system. If path $$ADB$$ is used
work done by the system is 10 $$J.$$ The heat Flow into the system in path $$ADB$$ is :
A.
40 $$J$$
B.
80 $$J$$
C.
100 $$J$$
D.
20 $$J$$
Answer :
40 $$J$$
Solution :
$$\eqalign{ & \Delta {Q_{ACB}} = \Delta {W_{ACB}} + \Delta {U_{ACB}} \cr & \Rightarrow \,\,60\,J = 30\,J + \Delta {U_{ACB}} \cr & \Rightarrow \,\,{U_{ACB}} = 30\,J \cr & \Delta {Q_{ADB}} = \Delta {U_{ADB}} + \Delta {W_{ADB}} \cr & = 10\,J + 30\,J\,\,\left[ {\because \,\,\Delta {U_{ADB}} = \Delta {U_{ACB}} = 30\,J} \right] \cr & = 40\,J \cr} $$
$$\eqalign{ & \Delta {Q_{ACB}} = \Delta {W_{ACB}} + \Delta {U_{ACB}} \cr & \Rightarrow \,\,60\,J = 30\,J + \Delta {U_{ACB}} \cr & \Rightarrow \,\,{U_{ACB}} = 30\,J \cr & \Delta {Q_{ADB}} = \Delta {U_{ADB}} + \Delta {W_{ADB}} \cr & = 10\,J + 30\,J\,\,\left[ {\because \,\,\Delta {U_{ADB}} = \Delta {U_{ACB}} = 30\,J} \right] \cr & = 40\,J \cr} $$
