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 $1.1T$, and the volume is increase to $1.05V$, the final pressure will be

• A. between $p$ and $1.1p$.
• B. $1.1p$
• C. $p$
• D. less than $p$

Answer 1

The correct option is A between $p$ and $1.1p$.

$\text{Formula Used}$: $PV=nRT$

Let $P_1=p,V_2=1.05V,V_1=V$,
$T_2=1.1T,T_1=T$

From ideal gas equation, $PV=nRT$.

Here $n$ is the numbers of moles,

So, $n=\frac{P_1{V}_1}{R{T}_1}=\frac{P_2{V}_2}{R{T}_2}$

Or $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

$P_2=P_1\frac{V_1}{V_2}\frac{T_2}{T_1}$

Substituting the values, we get

$\therefore P_2=\frac{p\times V\times 1.1T}{1.05V\times T}$

$=\frac{1.1}{1.05}p$

$=1.05p$

i.e. between $p$ and $1.1p$

$\text{Final Answer}:$ (d).