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 \( R = 8.3 \, {J K}^{-1} \, {mol}^{-1} \) Choose the correct answer from the options given below:

• 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 calculating the temperature change in a gas, use the formula \( Q = n C_V \Delta T \). The molar heat capacity for a monoatomic gas is \( \frac{3R}{2} \).

Answer 1

The Correct Option is C

We can use the formula for the heat absorbed by the gas: \[ Q = n C_V \Delta T \] Where: - \( Q = 500 \, {J} \) (heat transferred), - \( n = 0.5 \, {mol} \), - \( C_V = 3R/2 \) (molar heat capacity for a monoatomic gas, where \( R = 8.3 \, {J/mol·K} \)). First, calculate \( C_V \): \[ C_V = \frac{3}{2} \times 8.3 = 12.45 \, {J/mol·K} \] Now, solve for the temperature change \( \Delta T \): \[ 500 = 0.5 \times 12.45 \times \Delta T \] \[ \Delta T = \frac{500}{0.5 \times 12.45} = 80 \, {K} \] The final temperature: \[ T_f = 298 \, {K} + 80 \, {K} = 378 \, {K} \] The change in internal energy is \( \Delta U = 300 \, {J} \). Thus, the correct answer is (3) 378 K and 300 J.