Question

which equation below represents charless law?

\\(\frac{v_1}{t_1} = \frac{v_2}{t_2}\\)

\\(\frac{v_1}{t_2} = \frac{v_2}{t_1}\\)

\\(v_1 t_1 = p_2 t_2\\)

\\(p_1 v_1 t_1 = p_2 v_2 t_2\\)

Explanation:

<pre_analysis>
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"new_concepts": [
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"current_concepts": [
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</pre_analysis>

<reasoning>

State the definition of Charles's law

\[
V \propto T \quad \text{(at constant pressure and amount of gas)}
\]

Express the direct proportionality mathematically

\[
\frac{V}{T} = \text{constant}
\]

Formulate the relation for two states

\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)</mcq-correct>
<mcq-option>(B) \(\frac{V_1}{T_2} = \frac{V_2}{T_1}\)</mcq-option>
<mcq-option>(C) \(V_1 T_1 = P_2 T_2\)</mcq-option>
<mcq-option>(D) \(P_1 V_1 T_1 = P_2 V_2 T_2\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Natural Science",
"question_type": "Multiple Choice",
"knowledge_point": [
"Natural Science",
"Chemistry",
"Charles's Law"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
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],
"needs_drawing": false,
"concepts_used": [
"Gas Laws"
],
"new_concepts": [
"Charless Law"
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</pre_analysis>

<reasoning>

State the definition of Charles's law

\[
V \propto T \quad \text{(at constant pressure and amount of gas)}
\]

Express the direct proportionality mathematically

\[
\frac{V}{T} = \text{constant}
\]

Formulate the relation for two states

\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)</mcq-correct>
<mcq-option>(B) \(\frac{V_1}{T_2} = \frac{V_2}{T_1}\)</mcq-option>
<mcq-option>(C) \(V_1 T_1 = P_2 T_2\)</mcq-option>
<mcq-option>(D) \(P_1 V_1 T_1 = P_2 V_2 T_2\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Natural Science",
"question_type": "Multiple Choice",
"knowledge_point": [
"Natural Science",
"Chemistry",
"Charles's Law"
]
}
</post_analysis>