Hydrogen gas is filled in a balloon at 20°C. If temperature is made 40°C, pressure remaining same, what fraction of hydrogen will come out

The correct option is 0.07.

To find the fraction of hydrogen gas that escapes from the balloon when it is heated at constant pressure and volume, we can use the ideal gas law:
$PV=nRT$

Here, the pressure ($P$) remains constant, and we assume the capacity (volume, $V$) of the balloon remains constant. Since $R$ is the universal gas constant, the relation becomes:
$nT=\text{constant}$
or
$n_1{T}_1=n_2{T}_2$

where:
- $n_1$ is the initial number of moles of hydrogen gas.
- $n_2$ is the final number of moles of hydrogen gas left in the balloon.
- $T_1$ is the initial temperature in Kelvin.
- $T_2$ is the final temperature in Kelvin.

First, convert the temperatures from Celsius to Kelvin:
$T_1=20°\text{C}=20+273=293\text{K}$
$T_2=40°\text{C}=40+273=313\text{K}$

Now, calculate the final number of moles in terms of the initial moles:
$n_2=n_1\cdot \frac{T_1}{T_2}=n_1\cdot \frac{293}{313}$

The fraction of hydrogen gas that escapes (comes out) is given by:
$\text{Fraction escaped}=\frac{n_1-n_2}{n_1}=1-\frac{n_2}{n_1}$

Substituting the values:
$\text{Fraction escaped}=1-\frac{293}{313}=\frac{313-293}{313}=\frac{20}{313}\approx 0.064$

Comparing this value with the given options, the closest fraction is 0.07.