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: Problem Definition
A cylinder contains helium gas at standard temperature and pressure (STP). The cylinder's volume is 44.8 litres. Calculate the heat needed to increase the gas temperature by 20.0°C. 
Step 2: Moles Calculation 
At STP, 1 mole of an ideal gas occupies 22.4 litres. 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: Molar Heat Capacity at Constant Volume 
For monatomic helium, the molar heat capacity at constant volume (\( C_v \)) is: \[ C_v = \frac{3}{2} R. \] 
Using \( R = 8.3 \, \text{JK}^{-1} \text{mol}^{-1} \): \[ C_v = \frac{3}{2} \times 8.3 = 12.45 \, \text{JK}^{-1} \text{mol}^{-1}. \] 
Step 4: Heat Required Calculation 
The heat (\( Q \)) needed for a temperature increase \( \Delta T = 20.0°C \) is: \[ Q = n C_v \Delta T. \] 
Substituting values: \[ Q = 2 \times 12.45 \times 20 = 498 \, \text{J}. \] 
Step 5: Result Verification 
The calculated heat is 498 J, matching option (C). Final Answer: The required heat is 498 J.