Question 880: Thermodynamics & KTG

Question

A jar '$$\mathrm{P}$$' is filled with gas having pressure, volume and temperature $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ respectively. Another gas jar $$Q$$ filled with a gas having pressure $$2 \mathrm{P}$$, volume $$\frac{\mathrm{V}}{4}$$ and temperature $$2 \mathrm{~T}$$. The ratio of the number of molecules in jar $$\mathrm{P}$$ to those in jar $$Q$$ is

Accepted Answer

According to the ideal gas equation $$\mathrm{PV}=\mathrm{Nk}_{\mathrm{B}} \mathrm{T}$$
For jar $$\mathrm{P}$$, we have
$$\mathrm{PV}=\mathrm{N}_1 \mathrm{k}_{\mathrm{B}} \mathrm{T}$$ ..... (i)
For jar Q, we have,
(2P) $$\left(\frac{V}{4}ight)=\mathrm{N}_2 \mathrm{k}_{\mathrm{B}}(2 \mathrm{~T})$$
$$\Rightarrow \mathrm{PV}=4 \mathrm{~N}_2 \mathrm{k}_{\mathrm{B}} \mathrm{T}$$ ..... (ii)
From equations (i) and (ii)
$$\begin{aligned}
& N_1=4 N_2 \quad \Rightarrow \frac{N_1}{N_2}=4 \
	herefore \quad & N_1: N_2=4: 1
\end{aligned}$$

Answer

$$1: 1$$

Answer

$$1: 2$$

Answer

$$2: 1$$

Answer

$$4: 1$$

Thermodynamics & KTG

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