Question

A hydrogen cylinder is designed to withstand an internal pressure of $100\,atm$. At ${27^ \circ }C$ , hydrogen is pumped into the cylinder which exerts a pressure of $20\,atm$ . At what temperature does the danger of explosion first set in? $({P_1} = 20\,atm)$
A. $500\,K$
B. $1500\,K$
C. $1000\,K$
D. $2000\,K$

Answer 1

Complete answer:
An ideal gas law is also known as the general gas equation, it is the equation of state of ideal gas. It is a good approximation of the behavior of many gases under many conditions.
The state of an amount of gas is determined by its pressure, volume, and temperature.
The ideal gas is written as $PV = nRT$. Here P is pressure, V is volume, T is temperature, n is the amount of gas, and R is ideal gas constant. It is the same for all gases.
Here in the given question, volume is fixed for the hydrogen cylinder as it is closed, the amount of gas is also the same so our equation will become $P \propto T$. That means as pressure changes the temperature of the gas will also change and vice versa. Or we can mathematically write it as , $\dfrac{{{P_1}}}{{{T_1}}} = \dfrac{{{P_2}}}{{{T_2}}}$
Our question says, the initial pressure was ${P_1} = 20\,atm,$ when the pressure will reach to 100 the volume will be
So given in the question is ${P_1} = 20\,atm,{T_1} = {27^ \circ }C = 27 + 273 = 300\,K,{P_2} = 100\,atm,{T_2} = ?$
By putting the values in the equation, we get
$\dfrac{{20}}{{300}} = \dfrac{{100}}{{{T_2}}} \\\ T2 = 1500\,K$

**Therefore the correct option is B

Note:**
An ideal gas law is for ideal gases which are hypothetical. In an ideal world collisions between gases and molecules are completely elastic. But in reality, they interact with each other and hence show some deviation from ideal behavior. Gases behave much like ideal when they are at low pressure and temperature