A pressure cooker cooks a lot faster than an ordinary pan by maintaining a highe

Question

A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and temperature inside. The lid of a pressure cooker is well sealed, and steam can escape only through and opening in the middle of the lid. A seperate metal piece , the petcock, sits on top of this opening and prevents steam from escaping untill the pressure force overcomes the weight of the petcock. The periodic escape of the steam in this manner prevents any potentially dangerous pressure buildup and keeps the pressure inside at a constant value. Determine the mass of the petcock of a pressure cooker whose operations pressure is 100 KPa gage and has an opening cross-sectional area of 4 mm^2 . assume an atomspheric pressure of 101 KPa, and a draw of the petcock

answer 40.8 g

Explanation / Answer

pressure difference between the cooker and atmosphere is P gauge = 100 kpa = 100000 pa

force due to pressure is F = ( 100000 pa ) * ( 4 mm2 )= ( 100000 pa ) * ( 4 * 10- 6 * 10 mm2 )

F = 0.4 N

this force is balanced by the weight of the petcock ie F = mg

0.4 = m * 9.81

m = 0.04077 kg = 40.77 gm = 40.8 gm

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