Question

Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters \(2P\), \(\frac{V}{4}\), \(2T\). The ratio of number of molecules of jar B to those of jar A is

• A. \(1:2\)
• B. \(1:4\)
• C. \(2:1\)
• D. \(4:1\)

Hint:

Number of molecules is proportional to PV/T.

Answer 1

The Correct Option is B

Step 1: Use moles:
$n = \frac{PV}{RT}$. Compare $n_B$ and $n_A$.

Step 2: Numerator:
The product $PV$ changes by $2 \times \frac14 = \frac12$.

Step 3: Denominator:
The temperature doubles, giving another factor $\frac12$. Total factor $\frac12 \times \frac12 = \frac14$, so $N_B : N_A = 1 : 4$.

Final Answer:
The ratio is 1:4, option (B). \[ \boxed{1:4} \]