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Question
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
1.1 p
p
less than p
between p and 1.1.
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Solution
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 between p and 1.1.
Explanation:
According to the equation of ideal gas, PV = nRT
P = pressure
V = volume
n = Number of moles of gases
R = gas constant
T = temperature
Thus we have to rewrite this equation in such a way that no. of moles is given by,
`n = (PV)/(RT)`
The number of moles of the gas remain fixed, hence, we can write
`(P_1V_1)/(RT_1) = (P_2V_2)/(RT_2)`
⇒ `P_2 = (P_1V_1) (T/(V_2T_1))`
= `((P)(V)(1.1T))/((1.05)V(T))` .....`[(P_1 = P),(V_2 = 1.05 V and T_2 = 1.1T)]`
= `P xx ((1.1)/(1.05))`
= `P(1.0476) ≈ 1.05 P`
Hence, final pressure P2 lies between P and 1.1P.
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