KVPY SA Exam 2011 Question Paper

Question : 68 of 80

Marks: +1, -0

In a thermally isolated system, two boxes filled with an ideal gas are connected by a valve. When the valve is in closed position, states of the box 1 and 2, respectively, are (1 atm, V, T) and (0.5 atm, 4V, T). When the valve is opened, the final pressure of the system is approximately

0.5 atm
0.6 atm
0.75 atm
1.0 atm

Validate

Solution:

After opening of at equilibrium temperature and pressure of whole gas is

T_1

and

P_1

n_1={1×V}/{RT},n_2={0.5×V×4}/{RT}

n_1 + n_2 = n

V/{RT}+{V×4}/{2RT}={5VP_1}/{RT_1}

{3V}/{RT} ={5VP_1}/{RT_1}

P_1/T_1=0.6/T

∆Q = 0 , ∆W = 0
∴ ∆U = 0

n_1C_VT + n_2C_VT

= (n_1 + n_2)C_VT_1

T_1=T

P_1/T=0.6/T

P_1 = 0.6 \atm

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