Question

The pressure $( P )$ and temperature $( T )$ relationship of an ideal gas obeys the equation $PT ^2=$ constant The volume expansion coefficient of the gas will be :

• A. $3 T ^2$
• B. $\frac{3}{ T ^2}$
• C. $\frac{3}{ T ^3}$
• D. $\frac{3}{ T }$

Answer 1

Answer: (A)

$3 T ^2$

Answer 2

PT2= constant, Using
PV=nRT
P=VnRT​
PT2=VnRT​×T2= constant
⇒T3=KV
So, dTd​(KV)=3T2
⇒dTKdV​=3T2
⇒dV=K3T2​dT
dV=VγdT
⇒γ=KV23T2​=T33T2​=T3​