Question

At constant pressure, if equal amounts of heat are supplied to a monoatomic gas and a rigid diatomic gas, then the ratio of the changes in the internal energies of the monoatomic and diatomic gases is:

• A. \(3:5\)
• B. \(1:12\)
• C. \(1:25\)
• D. \(14:23\)

Hint:

For equal heat supplied: \[ \Delta U=Q\frac{C_V}{C_P}. \] Use specific heat ratios directly.

Answer 1

The Correct Option is D

Concept: For equal heat supplied, \[ Q=nC_P\Delta T. \] Change in internal energy: \[ \Delta U=nC_V\Delta T. \] Thus \[ \Delta U = Q\frac{C_V}{C_P}. \]

Step 1: Monoatomic gas.
\[ C_V=\frac32R, \qquad C_P=\frac52R. \] \[ \Delta U_M = Q\left(\frac{3}{5}\right). \]

Step 2: Rigid diatomic gas.
\[ C_V=\frac52R, \qquad C_P=\frac72R. \] \[ \Delta U_D = Q\left(\frac57\right). \]

Step 3: Take ratio.
\[ \frac{\Delta U_M}{\Delta U_D} = \frac{3/5}{5/7}. \] \[ = \frac{21}{25}. \] \[ \boxed{21:25} \]