Question

If R is the universal gas constant then the amount of heat needed to raise the temperature of 3 moles of an ideal monoatomic gas from 273 K to 393 K when no work is done is

• A. \(450\text{ R}\)
• B. \(500\text{ R}\)
• C. \(540\text{ R}\)
• D. \(570\text{ R}\)

Hint:

No work done means constant volume, so the heat equals n Cv times the temperature rise.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
When no work is done the volume is constant, so \(Q=nC_v\Delta T\).

Step 2: Molar specific heat
For a monoatomic ideal gas \(C_v=\dfrac{3}{2}R\).

Step 3: Calculation
\(\Delta T=393-273=120\text{ K}\)
\(Q=3\times\dfrac{3}{2}R\times120=540R\)

Final Answer:
The heat required is \(540R\). \[ \boxed{\text{(C) }540\text{ R}} \]