Question

Match the column with the correct numerical values of energy/heat in column-II (R is universal gas constant)

• A. A \( \rightarrow \) R; B \( \rightarrow \) P; C \( \rightarrow \) Q
• B. A \( \rightarrow \) P; B \( \rightarrow \) R; C \( \rightarrow \) Q
• C. A \( \rightarrow \) R; B \( \rightarrow \) Q; C \( \rightarrow \) P
• D. A \( \rightarrow \) Q; B \( \rightarrow \) P; C \( \rightarrow \) R

Hint:

For ideal gases, use the formulas for specific heat and internal energy to calculate the required quantities.

Answer 1

The Correct Option is A

To match the columns and find the correct numerical values, we will need to analyze each item in Column-I and relate it to the appropriate value from Column-II using the properties of gases and their specific heat capacities.

1. (A) 1 mole of monatomic ideal gas undergoes:

For a monatomic ideal gas, such as helium or argon, the change in internal energy (ΔU) is given by:

\(ΔU = \frac{3}{2}nRΔT\).

Since the gas is undergoing a change involving 1 mole, we have:

\(ΔU = 1 \times \frac{3}{2}RΔT = \frac{3}{2}RΔT.\)

Matching this with options, we find (R) 480R fits as it aligns with the calculated form: (A) → R.

1. (B) Find heat supplied to 2 moles of gas having:

For heat supplied to a gas, the formula is:

\(Q = nC_vΔT\) for constant volume.

For an ideal diatomic gas:

\(C_v = \frac{5}{2}R\).

Thus,

\(Q = 2 \times \frac{5}{2}RΔT = 5RΔT.\)

So, option (P) 650R is a match: (B) → P.

1. (C) Find the ΔU for 1 mole diatomic:

For diatomic gases, internal energy change is:

\(ΔU = \frac{5}{2}nRΔT.\)

When n = 1, it is simply:

\(ΔU = \frac{5}{2}RΔT.\)

Matching with options, (Q) 800R matches the proportionality: (C) → Q.

Thus, the correct matching is: A → R; B → P; C → Q.