Two closed vessels of equal volume containing air at pressure P1 and temperature T1, are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at T1 and that in the other at T2, what will be the pressure in the vessels?

Question

Two closed vessels of equal volume containing air at pressure P1 and temperature T1, are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at T1 and that in the other at T2, what will be the pressure in the vessels? (A) (2P1 T1/T1+T2) (B) (T1/2P1T2) (C) (2P1T2/T1+T2) (D) (2P1/T1+T2)

Tardigrade Admin · Accepted Answer

(P1/T1)+(P1/T1)=(P/T1)+(P/T2) (2P1/T1)=P((T1 +T2/T1T2)) ∴ P=(2P1(T1T2)/T1(T1+T2))=(2P1T2/T1+T2)

Q. Two closed vessels of equal volume containing air at pressure $P_{1}$ and temperature $T_{1}$ , are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at $T_{1}$ and that in the other at $T_{2}$ , what will be the pressure in the vessels?

$\frac{2 P _{1} T _{1}}{T _{1} + T _{2}}$

$\frac{T _{1}}{2 P _{1} T _{2}}$

$\frac{2 P _{1} T _{2}}{T _{1} + T _{2}}$

$\frac{2 P _{1}}{T _{1} + T _{2}}$

$\frac{P _{1}}{T _{1}} + \frac{P _{1}}{T _{1}} = \frac{P}{T _{1}} + \frac{P}{T _{2}}$
$\frac{2 P _{1}}{T _{1}} = P (\frac{T _{1} + T _{2}}{T _{1} T _{2}})$
$∴ P = \frac{2 P _{1} ( T _{1} T _{2} )}{T _{1} ( T _{1} + T _{2} )} = \frac{2 P _{1} T _{2}}{T _{1} + T _{2}}$

Q. Two closed vessels of equal volume containing air at pressure P1​ and temperature T1​, are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at T1​ and that in the other at T2​, what will be the pressure in the vessels?

T1​+T2​2P1​T1​​

2P1​T2​T1​​

T1​+T2​2P1​T2​​

T1​+T2​2P1​​