Question:
The heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by \(48 ^{\circ}\text{C}\) at constant pressure is (\(R\) = gas constant, Molecular weight of nitrogen \((\text{N}_2)\) = 28)
The heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by \(48 ^{\circ}\text{C}\) at constant pressure is (\(R\) = gas constant, Molecular weight of nitrogen \((\text{N}_2)\) = 28)
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\(Q=nC_p\Delta T\) with \(C_p=\frac72R\) for a diatomic gas.
Updated On: Oct 1, 2026
- \(72 R\)
- \(84 R\)
- \(96 R\)
- \(108 R\)
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Nitrogen is a diatomic gas, so \(C_p=\dfrac72R\).
Step 2: Key Formula or Approach
\(n=\dfrac{14}{28}=0.5\) mol and \(Q=nC_p\Delta T\).
Step 3: Detailed Explanation
\[ Q=0.5\times\frac72R\times48=0.5\times3.5\times48\,R=84R \]
Final Answer:
The heat needed is \(84R\), option (B). \[ \boxed{84R\ \text{(B)}} \]
Nitrogen is a diatomic gas, so \(C_p=\dfrac72R\).
Step 2: Key Formula or Approach
\(n=\dfrac{14}{28}=0.5\) mol and \(Q=nC_p\Delta T\).
Step 3: Detailed Explanation
\[ Q=0.5\times\frac72R\times48=0.5\times3.5\times48\,R=84R \]
Final Answer:
The heat needed is \(84R\), option (B). \[ \boxed{84R\ \text{(B)}} \]
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