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)

• A. \(72 R\)
• B. \(84 R\)
• C. \(96 R\)
• D. \(108 R\)

Hint:

\(Q=nC_p\Delta T\) with \(C_p=\frac72R\) for a diatomic gas.

Answer 1

The Correct Option is B

Step 1: Use $C_p=C_v+R$
$C_v=\tfrac52R$, so $C_p=\tfrac72R$.

Step 2: Multiply
$Q=\tfrac12\times\tfrac72R\times48=\tfrac{7\times48}{4}R=84R$, option (B).

Final Answer:
The heat is $84R$, option (B). \[ \boxed{84R} \]