Question 865: Thermodynamics & KTG

Question

We have a jar filled with gas characterized by parameters $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ and another jar B filled with gas having parameters $$2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

Accepted Answer

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

Answer

$$1: 1$$

Answer

$$1: 2$$

Answer

$$2: 1$$

Answer

$$4: 1$$

Thermodynamics & KTG

We have a jar filled with gas characterized by parameters $\mathrm{P}, \mathrm{V}, \mathrm{T} and another jar B filled with gas having parameters 2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}$, where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

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