Question 49: Thermodynamics & KTG

Question

A cylinder of fixed capacity 44.81 contains hydrogen gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $$20^{\circ} \mathrm{C}$$ ? ($$R=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$)

Accepted Answer

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 $$20^{\circ} 	ext{C}$$. WeÃ¢ÂÂ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 (HÃ¢ÂÂ) 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, $$n$$:
$$ n = \frac{	ext{Volume of gas}}{	ext{Volume of one mole at STP}} = \frac{44.81 \, 	ext{L}}{22.4 \, 	ext{L/mol}} = 2 \, 	ext{mol} $$
2.
Use the specific heat capacity at constant volume (CÃ¢ÂÂ):
For hydrogen gas (HÃ¢ÂÂ), which is diatomic, the molar heat capacity at constant volume $$C_V$$ is:
$$ C_V = \frac{5}{2} R $$
where $$R = 8.31 \, 	ext{J} \, 	ext{mol}^{-1} \, 	ext{K}^{-1}$$. So:
$$ C_V = \frac{5}{2} 	imes 8.31 \, 	ext{J} \, 	ext{mol}^{-1} \, 	ext{K}^{-1} = 20.775 \, 	ext{J} \, 	ext{mol}^{-1} \, 	ext{K}^{-1} $$
3.
Calculate the heat required:
The heat required $$Q$$ to raise the temperature of the gas by $$\Delta T = 20^{\circ} 	ext{C}$$ (which is the same in Kelvin) is given by the formula:
$$ Q = n \cdot C_V \cdot \Delta T $$
Plugging in the values:
$$ Q = 2 \, 	ext{mol} 	imes 20.775 \, 	ext{J} \, 	ext{mol}^{-1} \, 	ext{K}^{-1} 	imes 20 \, 	ext{K} = 831 \, 	ext{J} $$
Thus, the amount of heat needed to raise the temperature of the hydrogen gas in the cylinder by $$20^{\circ} 	ext{C}$$ is
831 J
.
Therefore, the correct option is:
Option C: 831 J

Answer

541 J

Answer

374 J

Answer

831 J

Answer

743 J

Thermodynamics & KTG

A cylinder of fixed capacity 44.81 contains hydrogen gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by $20^{\circ} \mathrm{C} ? (R=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$)

Choose the correct answer: