Question

Identify the correct equation relating \( \Delta H \), \( \Delta U \), and \( \Delta T \) for 1 mole of an ideal gas (R = gas constant):

• A. \( (\Delta H)^2 = \Delta U + R \Delta T \)
• B. \( \Delta H = (\Delta U)^2 + R \Delta T \)
• C. \( \Delta U = \Delta H - R \Delta T \)
• D. \( \Delta U = \Delta H + R \Delta T \)

Hint:

For an ideal gas, the relationship between enthalpy, internal energy, and temperature change follows \( \Delta H = \Delta U + R \Delta T \).

Answer 1

The Correct Option is C

Step 1: Apply the First Law of Thermodynamics for an Ideal Gas For an ideal gas: \[ \Delta H = \Delta U + R \Delta T \] Rearrange to solve for \( \Delta U \): \[ \Delta U = \Delta H - R \Delta T \] Thus, the correct answer is \( \Delta U = \Delta H - R \Delta T \).