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:
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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 \( \frac{3R}{2} \).
The heat absorbed by the gas is calculated using the formula \( Q = n C_V \Delta T \), where \( Q = 500 \, {J} \), \( n = 0.5 \, {mol} \), and \( C_V = 3R/2 \) for a monoatomic gas with \( R = 8.3 \, {J/mol·K} \). The molar heat capacity \( C_V \) is \( 12.45 \, {J/mol·K} \) (\(\frac{3}{2} \times 8.3\)). The temperature change \( \Delta T \) is \( 80 \, {K} \), derived from \( 500 = 0.5 \times 12.45 \times \Delta T \), which simplifies to \( \Delta T = \frac{500}{0.5 \times 12.45} \). The final temperature is \( T_f = 298 \, {K} + 80 \, {K} = 378 \, {K} \). The change in internal energy is \( \Delta U = 300 \, {J} \). Therefore, the correct answer is 378 K and 300 J.
