Question:medium
The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by $48^\circ C$ at constant pressure is (Molecular weight of nitrogen = 28, R = gas constant, $C_p = 7/2 R$ for diatomic gas) ______.
The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by $48^\circ C$ at constant pressure is (Molecular weight of nitrogen = 28, R = gas constant, $C_p = 7/2 R$ for diatomic gas) ______.
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Always watch out for $C_p$ vs $C_v$! If the container was rigid/sealed (constant volume), you would use $C_v = \frac{5}{2} R$ instead, yielding $60R$. Read the constraint ("constant pressure") carefully!
Updated On: Jun 19, 2026
- 76 R
- 84 R
- 90 R
- 96 R
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Heat supplied at constant pressure is $Q = n C_p \Delta T$.
Step 2: Formula Application:
Number of moles $n = \frac{\text{Mass}}{\text{Molecular Weight}} = \frac{14}{28} = 0.5$ moles.
Step 3: Explanation:
$Q = 0.5 \times \frac{7}{2}R \times 48$. $Q = 0.5 \times 7R \times 24 = 3.5R \times 24 = 84R$.
Step 4: Final Answer:
The heat energy required is 84 R.
Heat supplied at constant pressure is $Q = n C_p \Delta T$.
Step 2: Formula Application:
Number of moles $n = \frac{\text{Mass}}{\text{Molecular Weight}} = \frac{14}{28} = 0.5$ moles.
Step 3: Explanation:
$Q = 0.5 \times \frac{7}{2}R \times 48$. $Q = 0.5 \times 7R \times 24 = 3.5R \times 24 = 84R$.
Step 4: Final Answer:
The heat energy required is 84 R.
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