500 J of energy is transferred as heat to 0. | vedclass

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Question

(A) Argon is a monoatomic gas,so $C_v = \frac{3}{2}R$ and $C_p = \frac{5}{2}R$. Since the process occurs at constant pressure $(1.00 \ atm)$,the heat

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$348 \ K$ and $300 \ J$

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(A) Argon is a monoatomic gas,so $C_v = \frac{3}{2}R$ and $C_p = \frac{5}{2}R$. Since the process occurs at constant pressure $(1.00 \ atm)$,the heat transferred is $q_p = n 	imes C_p 	imes \Delta T$. $500 = 0.5 	imes (\frac{5}{2} 	imes 8.3) 	imes (T_f - 298)$. $500 = 10.375 	imes (T_f - 298)$. $T_f - 298 = 48.19 \ K \Rightarrow T_f \approx 346.2 \ K$. However,checking the options,let us re-evaluate using $C_p = \frac{5}{2}R \approx 20.75 \ J \ K^{-1} \ mol^{-1}$. $500 = 0.5 	imes 20.75 	imes \Delta T \Rightarrow \Delta T = 48.19 \ K$. $T_f = 298 + 48.19 = 346.19 \ K$. For internal energy change: $\Delta U = n 	imes C_v 	imes \Delta T = 0.5 	imes (\frac{3}{2} 	imes 8.3) 	imes 48.19 \approx 300 \ J$. Given the options provided,$348 \ K$ is the closest value to $346.2 \ K$ and $\Delta U = 300 \ J$ is correct.

$500 \ J$ 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 $: R = 8.3 \ J \ K^{-1} \ mol^{-1}$

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