Question

Find 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. (Molecular weight of nitrogen = 28; \(R\) is the gas constant; \(C_p = \frac{7}{2}R\) for a diatomic gas.)

Hint:

Always identify if the gas is monoatomic or diatomic to verify \(C_p\). Nitrogen (\(N_2\)) is diatomic. Also, remember that for calculating heat energy, the change in temperature in Celsius is identical to the change in Kelvin.

Answer 1

Step 1: Understanding the Question:
Heat supplied at constant pressure is calculated using the number of moles and molar heat capacity.
Step 2: Key Formula or Approach:
\( \Delta Q = n C_p \Delta T \).
Step 3: Detailed Explanation:
Moles \( n = \frac{14}{28} = 0.5 \) mol.
\( \Delta T = 48 \text{ K} \).
\( C_p = 7/2 R \).
\[ \Delta Q = 0.5 \cdot \frac{7}{2}R \cdot 48 = \frac{1}{2} \cdot \frac{7}{2} \cdot 48 \cdot R = \frac{7}{4} \cdot 48 \cdot R = 84R \]
Step 4: Final Answer:
Heat energy is \( 84R \).