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: [2025]

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Solution

Q.
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: [2025]

1 378 K and 300 J

2 348 K and 300 J

3 368 K and 500 J

4 378 K and 500 J

Ans.
(2)

As heat is transferred at constant pressure, all the heat transferred changes enthalpy of the system.

$q_{p} = Δ H$

$500 = n C_{p} Δ T$

$500 = 0.5 \times \frac{5}{2} R \times (T_{f} - 298)$

$500 = 0.5 \times \frac{5}{2} \times 8.3 \times (T_{f} - 298)$

$T_{f} = 346.19 K$

$\frac{Δ U}{Δ H} = \frac{n C_{v} Δ T}{n C_{p} Δ T} = \frac{n (\frac{3}{2}) R Δ T}{n (\frac{5}{2}) R Δ T} = \frac{3}{5}$

$\frac{Δ U}{500} = \frac{3}{5}$

$Δ U = 300$ $J$

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