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

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

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

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

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}}

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

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

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

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

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

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

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

= P (1.0476) \approx 1.05 P

$= P (1.0476) \approx 1.05 P$

Hence, the final pressure

P_{2}

$P_{2}$ lies between p and 1.1p.

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