Air is pumped into an automobile tyre’s tube up to a pressure of 200 kPa in the morning when the air temperature is 20°C. During the day the temperature rises to 40°C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature.

We know ideal gas equation


PV=nRT


Where V= volume of gas


R=gas constant


T=temperature


n=number of moles of gas


P=pressure of gas


Given


Pressure at temperature 20 P1=200Pa


Volume at temperature 20 =V1


Increase in volume =2%V1


Volume at temperature 40 V2=V1+2%V1


V2=V1+0.02V1=1.02V1


20=293.15K


40=313.15K


From ideal gas equation, we can write



Since, tube got expanded by the end of the day, only volume will change. Number of moles remains the same, before and after expansion as no new gas has been added. So, the product of nR will be same before and after expansion.




Pressure of the tube at 400C is 209.45kPa.


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