Thermodynamics

JEE Main level, single correct, medium

105 of 190

Question 105 of 190

A bicycle tyre is filled with air having pressure of 270kPa270kPa at 27∘C27^{\circ}C. The approximate pressure of the air in the tyre when the temperature increases to 36∘C36^{\circ}C is

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Answer: (C) 278kPa278kPa

Given here, P1=270kPa,T1=27+273=300K,T2=36+273=309K{P}_{1}=270kPa,{T}_{1}=27+273=300K,{T}_{2}=36+273=309K
Ideal gas equation is given by PV=nRTPV=nRT.
Considering isochoric process, i.e., constant volume so P∝TP\propto T
Thus, P1T1=P2T2\dfrac{{P}_{1}}{{T}_{1}}=\dfrac{{P}_{2}}{{T}_{2}}
⇒P2=P1T1×T2=270×(309)300\Rightarrow {P}_{2}=\dfrac{{P}_{1}}{{T}_{1}}\times {T}_{2}=\dfrac{270\times \left(309\right)}{300}
=278kPa=278kPa

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