Q19 of 27 Page 87

Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump ∆V (V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P1 to P2?

Let’s understand the situation first.


Here, as air is filled adiabatically, so there is no involvement of heat in the work equation.


We know that for adiabatic compression or expansion



As according to question is filled every time in the tube , but the volume is not increasing, so P must be increasing.


Just for instance before affect the pressure we can write


.............(1)


But after it affects P,


.............(2)


Because the process is adiabatic equation 1 and 2 should be equal





(cancelling out


on both sides)


As applying binomial expansion in the right hand side, which states that,








Work done is given by,


W




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