An inflated rubber ballon contains one mole of an ideal gas , has a pressure P, volume V and temperature T. If the temperature rises to 1.1 T, and the volume isincreased to 1.05 V, the final pressure will be

Options

A. 1.1 p
B. p
C. Less than p
D. between p and 1.1

Explanation

we know for an ideal gas , pV =nRT
`rArr " " n=` Number of moles ,p = Pressure V= Volume
R = Gas constnat , T= Temperature
`=(pV)/(RT)`
As number of moles of the gas remains fixed hence we can write
`(P_(1) V_(1))/(RT_(1)) =(p_(2) V_(2))/(RT_(2))`
`rArr" " P_(2) =(P_(1) V_(1)) ((T_(2))/(V_(2)T_(1)))`
`=((p)(v) (1.1T))/((1.05) V(T)) " "[overset(p_(1) =P)(V_(2)=1.05V) and T_(2) = 1.1 T]`
`=Pxx ((1.1)/(1.05))`
`=P(1.0476)~~ 1.05 p`
Hence final pressure `P_(2)` lies between p and 1.1p.