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Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied, $\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system
| Process | Condition |
| $(I)$ Adiabatic | $(A)\; \Delta W =0$ |
| $(II)$ Isothermal | $(B)\; \Delta Q=0$ |
| $(III)$ Isochoric | $(C)\; \Delta U \neq 0, \Delta W \neq 0 \Delta Q \neq 0$ |
| $(IV)$ Isobaric | $(D)\; \Delta U =0$ |
$I-B, II-D, III-A, IV-C$
$I-B, II-A, III-D, IV-C$
$I - A , II - A , III - B , IV - C$
$I - A , II - B , III - D , IV - D$
Solution
$(I)$ Adiabatic process $\Rightarrow \Delta Q=0$ No exchange of heat takes place with surroundings
$(II)$ Isothermal proess $\Rightarrow$ Temperature remains constant $(\Delta T =0)$
$\Delta u =\frac{ F }{2} nR \Delta T \Rightarrow \Delta u =0$
No change in internal energy $[\Delta u =0]$
$(III)$ Isochoric process Volume remains constant
$\Delta V =0$
$W =\int P \cdot d V =0$
Hence work done is zero.
$(IV)$ Isobaric process $\Rightarrow$ Pressure remains constant
$W = P . \Delta V \neq 0$
$\Delta u =\frac{ F }{2} nR \Delta T =\frac{ F }{2}[ P \Delta V ] \neq 0$
$\Delta Q = n C _{ p } \Delta T \neq 0$
