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Q.

On the $P - T$ graph of an ideal gas,

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a

adiabatic curve will have a positive slope

b

the slope of adiabatic curve will decrease with increase in $T$

c

adiabatic process will be a straight line

d

isochoric process will be a straight line passing through the origin

answer is B, C.

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Detailed Solution

Ideal gas

$PV = RT \Rightarrow V = \frac{R T}{P}$

Adiabatic:

${PV}^{γ} = c o n s \tan t \Rightarrow P {(\frac{R T}{P})}^{γ} = c o n s \tan t \Rightarrow P^{1 - γ} T^{γ} = c o n s \tan t \Rightarrow P = c^{\cdot} \cdot T^{\frac{γ}{γ - 1}} ∴ s l o p e = \frac{d P}{d t} = \frac{c γ}{γ - 1} T^{\frac{1}{γ - 1}} > 0 (n o t c o n s \tan t)$

$\frac{d^{2} P}{d T^{2}} > 0$

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