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Question

A pressure cooker of volume 10 litres contains an ideal gas at atmospheric pressure 105 Pa and temperature of 27°C. It has a whistle which has an area of 0.1 cm2 and mass of 100 gm. To what temperature should it be heated so that the whistle is just lifted up? 
 
  1. 580 K
  2. 500 K
  3. 470 K
  4. 600 K


Solution

The correct option is D 600 K
Given, V1=10 l,P=105,T1=27oC,m=100 g,A=0.1 cm

Using the ideal gas equation, pv=nRT
So, P2V2=nRT2T2=P2V2nR...(1)

Similarly as P1V1=nRT1n=P1V1RT1=105×VR×300

Now the pressure in cooker = P2=P0+mgA=105+100×103×100.1×104P2=2×105 Pa

Using P2 and n values in eq.(1)
T2=2×105×V×R×300R×105×VT2=600 K

 

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