An inflated rubber balloon 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 is increased to 1.05 V, the final pressure will be

Options

A. 1.1p
B. P
C. Less than p
D. Between p and 1.1p

Answer

D

Explanation

We know for an ideal gas `pV=nRT` (Ideal gas equation)
`rArrn` = Number of moles, p = Pressure, V = Volume
R = Gas constant, T = Termperature
`n=(pV)/(RT)`
As number of moles of the gas remains fixed, hence we can write
`(p_1V_1)/(RT_1)=(p_2V_2)/(RT_2)`
`rArrp_2=(p_1V_1)(T_2/(V_2T_1))`
`=((p)(V)(1.1T))/((1.05)V(T))" "[{:(p_1=p),(V_2=1.05 and T_2=1.1T):}]`
`=pxx((1.1)/(1.05))`
`=p(1.0476)~~1.05p`
Hence, final pressure `p_2` lies between p and 1.1 p