Question

500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are: Given \( R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \).

• A. 348 K and 300 J
• B. 378 K and 500 J
• C. 378 K and 300 J
• D. 368 K and 500 J

Hint:

For ideal gases, the change in internal energy can be calculated by considering the specific heat capacity and the change in temperature.

Answer 1

The Correct Option is C

- The heat added to the system is used to increase the temperature of the gas, and also contributes to the change in internal energy. 

- Using the formula \( Q = nC_V \Delta T \), where \( Q = 500 \, \text{J} \), \( n = 0.5 \, \text{mol} \), and \( C_V \) (molar heat capacity at constant volume for Argon) can be calculated as \( C_V = \frac{3}{2} R \). 

- The temperature increase \( \Delta T \) is calculated as \( \Delta T = \frac{Q}{nC_V} \), resulting in a final temperature of 378 K.

 Thus, the final temperature is 378 K, and the change in internal energy is 300 J.