COMEDK 2023 Shift 1 Paper

To solve this problem, we can apply the ideal gas law, which states:
P⋅V=n⋅R⋅T
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
In the given problem, we have a closed vessel, meaning the volume V and the number of moles n are constant. So, changes in temperature will directly affect the pressure based on the equation:
‌

P1

T1

=‌

P2

T2

Where:
P1 and T1 are the initial pressure and temperature, respectively.
P2 and T2 are the final pressure and temperature, respectively.
The temperatures given in the question are in Celsius, so first convert them into Kelvin by adding 273.15:
‌T1=54∘C+273.15=327.15K
‌T2=1254∘C+273.15=1527.15K
Now using the formula:
‌‌

P2

P1

=‌

T2

T1

‌‌

P2

P1

=‌

1527.15

327.15

≈4.67
Thus, the pressure of the gas becomes approximately 4.67 times its original pressure.
The correct answer, therefore, is Option C, 4.67 times P1.