COMEDK 2024 Shift 2 Paper

To solve this problem, we need to determine the amount of heat required to raise the temperature of the hydrogen gas in the cylinder by 20∘C. We'll start by using the given data and applying the necessary equations from thermodynamics. Let's break down the steps:
1. Calculate the number of moles of hydrogen gas (H2) at STP:
At STP (Standard Temperature and Pressure), the volume of one mole of an ideal gas is 22.4 liters. Given the cylinder has a fixed capacity of 44.81 liters, we can find the number of moles, n :
2. Use the specific heat capacity at constant volume (Ct) :
For hydrogen gas (H2), which is diatomic, the molar heat capacity at constant volume CV is: CV=‌

5

2

R
where R=8.31Jmol−1K−1. So:
3. Calculate the heat required:
The heat required Q to raise the temperature of the gas by ∆T=20∘C (which is the same in Kelvin) is given by the formula:
Q=n⋅CV⋅∆T
Plugging in the values:
Thus, the amount of heat needed to raise the temperature of the hydrogen gas in the cylinder by 20∘C is 831 J .
Therefore, the correct option is:
Option C: 831 J