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: Use internal energy
At constant volume $Q=\Delta U=\dfrac{f}{2}nR\Delta T$ with $f=3$.

Step 2: Substitute
$Q=\dfrac{3}{2}\times3\times R\times120=540R$.

Step 3: Compare the options
Using $C_p=\dfrac{5}{2}R$ would give $900R$, which is not offered, so $540R$ is the right value.

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