Two identical vessels are connected by a tube with a valve letting the gas from one vessel into the other if the pressure difference `Delta p ge 1.10 atm`. Initially there was a vacuum in one vessel while the other contained ideal gas at a temperature `t_1 = 27 ^@C` and pressure `p_1 = 1.00 atm`. Then both vessels were heated to a temperature `t_2 = 10.7 ^@C`. Up to what value will the pressure in the first vessel (which had vacuum initially) increase ?

Explanation

Let `m_1` be the mass of the gas enclosed.
Then, `p_1 V = v_1 R T_1`
When heated some gas, passes into the evacuated vessel till pressure difference becomes `Delta p`. Let `p'_1` and `p'_2` be the pressure on the two sides of the valve. Then `p'_1 V = v'_1 R T_2` and
`p'_2 V = v'_2 R T_2 = (v_1 - v'_1) R T_2`
`p'_2 = ((p_1 V)/(R T_1) - (p'_1 V)/(R T_2))` or `p'_2 = ((p_1)/(T_1) -(p'_1)/(T_2))T_2`
But `p'_1 - p'_2 = Delta p`
So, `p'_2 = ((p_1)/(T_1) - (p'_2 + Delta p)/(T_2))T_2`
=`(p_1 T_2)/(T_1) - p'_2 - Delta p`
or, `p'_2 = (1)/(2) ((p_1 T_2)/(T_1) - Delta p) = 0.08 atm`.