Question

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be:

• A. 249 J
• B. 415 J
• C. 498 J
• D. 830 J

Hint:

For monatomic gases like helium, the molar heat capacity at constant volume is \( \frac{3}{2} R \). The heat required to change the temperature of a gas can be calculated using \( Q = n C_v \Delta T \), where \( n \) is the number of moles, \( C_v \) is the molar heat capacity at constant volume, and \( \Delta T \) is the change in temperature.

Answer 1

The Correct Option is C

Step 1: Understanding the Problem 
A cylinder contains helium gas at standard temperature and pressure (STP). The volume of the cylinder is 44.8 litres. We need to calculate the amount of heat required to raise the temperature of the gas by 20.0°C. 
Step 2: Calculating the Number of Moles of Helium 
At STP, 1 mole of an ideal gas occupies 22.4 litres. Therefore, the number of moles (\( n \)) of helium in 44.8 litres is: \[ n = \frac{44.8 \, \text{litres}}{22.4 \, \text{litres/mol}} = 2 \, \text{moles}. \] 
Step 3: Using the Heat Capacity at Constant Volume 
For a monatomic gas like helium, the molar heat capacity at constant volume (\( C_v \)) is: \[ C_v = \frac{3}{2} R. \] 
Given \( R = 8.3 \, \text{JK}^{-1} \text{mol}^{-1} \): \[ C_v = \frac{3}{2} \times 8.3 = 12.45 \, \text{JK}^{-1} \text{mol}^{-1}. \] 
Step 4: Calculating the Heat Required 
The heat (\( Q \)) required to raise the temperature by \( \Delta T = 20.0°C \) is: \[ Q = n C_v \Delta T. \] 
Substituting the values: \[ Q = 2 \times 12.45 \times 20 = 498 \, \text{J}. \] 
Step 5: Matching with the Options 
The calculated heat required is 498 J, which corresponds to option (C). Final Answer: The amount of heat needed is 498 J.