Question

Four molecules of a diatomic gas are heated from $0°\mathrm{C}$ to $50°\mathrm{C}$. Find the heat supplied to the gas if work done by it is zero.

• A. $780R$
• B. $500R$
• C. $100R$
• D. $650R$

Answer 1

The correct option is B

$500R$

The above numerical can be solved as:

Step 1:

Foe a diatomic molecule

$$\begin{gathered} {\mathrm{C}}_{\mathrm{v}}=5\mathrm{R}/2 \\ {\mathrm{C}}_{\mathrm{p}}=7\mathrm{R}/2 \end{gathered}$$

Step 2:

Number of moles, $\mathrm{n}=4$

$∆\mathrm{T}=50$

Since the process is isochoric, work done $=0$

Step 3:

In an isochoric process, $$\begin{gathered} \mathrm{Q}=∆\mathrm{U} \\ ={\mathrm{nC}}_{\mathrm{v}}∆\mathrm{T} \end{gathered}$$

Step 4:

$$\begin{gathered} \mathrm{Q}=\left(4\right)\times \left(\frac{5R}{2}\right)\times \left(50\right) \\ =500\mathrm{R} \end{gathered}$$

The heat supplied to the gas if work done by zero is $500\mathrm{R}$.

Hence, option B is correct.