Question

# The process $$CD$$ is shown in the diagram. As system is taken from $$C$$ to $$D$$, what happens to the temperature of the system?

A
Temperature first decreases and then increases
B
Temperatures first increases and then decreases
C
Temperature decreases continuously
D
Temperature increases continuously

Solution

## The correct option is A Temperature first decreases and then increasesSolution:- (A) temperature first decreases and then increasesFrom ideal gas equation,$$PV = nRT$$$$\Rightarrow T = \cfrac{PV}{nR}$$Let $$P$$ be the mid point on $$CD$$.At point C-$$P = 3 {p}_{0}$$$$V = {v}_{0}$$$$\therefore {T}_{C} = \cfrac{3{p}_{0} {v}_{0}}{nR} ..... \left( 1 \right)$$At mid-point P-$$P = \cfrac{{p}_{0} + 3 {p}_{0}}{2} = 2 {p}_{0}$$$$V = \cfrac{{v}_{0} + 3 {v}_{0}}{2} = 2 {v}_{0}$$$$\therefore {T}_{P} = \cfrac{4 {p}_{0} {v}_{0}}{nR} ..... \left( 2 \right)$$At point D-$$P = {p}_{0}$$$$V = 3 {v}_{0}$$$$\therefore {T}_{D} = \cfrac{3 {p}_{0} {v}_{0}}{nR} ..... \left( 3 \right)$$Now from $${eq}^{n} \left( 1 \right), \left( 2 \right) \& \left( 3 \right)$$, we have$${T}_{C} < {T}_{P} > {T}_{D}$$Hence the temperature will first decreases and then increases.Chemistry

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