Ncert Exercises & Solutions

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 \(1.1T,\) and the volume is increased to \(1.05V,\) the final pressure will be:

1.	\(1.1P\)
2.	\(P\)
3.	less than \(P\)
4.	between \(P\) and \(1.1P\)

(d) Hint: Use the ideal gas equation.

We know for an ideal gas, pV =nRT (Ideal gas equation)

\Rightarrow

n= Number of moles, p = Pressure, V = Volume, R =Gasconstant, T =Temperature

n = \frac{p V}{R T}

Step 1: Find the final pressure in the balloon.

As the number of moles of the gas remains fixed, hence, we can write:

\frac{P_{1} V_{1}}{R T_{1}} = \frac{P_{2} V_{2}}{R T_{2}}

\Rightarrow P_{2} = (P_{1} V_{1}) (\frac{T_{2}}{V_{2} T_{1}})

= \frac{(P) (V) (1.1 T)}{(1.05) V (T)} [P_{1} = P]

= P \times (\frac{1.1}{1.05})

= P (1.0476) \approx 1.05 P

Hence, the final pressure

P_{2}

lies between p and 1.1p.

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