Question 670: Thermodynamics & KTG

Question

The pressure ' P ', volume ' V ' and temperature ' T ' of a gas in a jar ' $A$ ' and the gas in other jar ' $B$ ' is at pressure ' 2 P ', volume ' V ' and temperature ' $\frac{T}{4}$ '. Then the ratio of the number of molecules in jar A and jar B will be

Accepted Answer

According to the gas equation, $\mathrm{PV}=\mathrm{Nk}_{\mathrm{B}} \mathrm{T}$ For first sample, we have,
$$ \mathrm{PV}=\mathrm{N}_1 \mathrm{k}_{\mathrm{B}} \mathrm{~T} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$$
For the second sample, we have,
$$ (2 \mathrm{P})\left(\frac{\mathrm{V}}{4}ight)=\mathrm{N}_2 \mathrm{k}_{\mathrm{B}}\left(\frac{\mathrm{~T}}{4}ight) $$
$$ \Rightarrow \quad P V=\frac{N_2 k_B T}{2} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(ii)$$
$	herefore \quad$ From equations (i) and (ii),
$$ \mathrm{N}_1=\frac{\mathrm{N}_2}{2} \Rightarrow \frac{\mathrm{~N}_1}{\mathrm{~N}_2}=\frac{1}{2} $$

Answer

$1: 1$

Answer

$1: 2$

Answer

$2: 1$

Answer

$4: 1$

Thermodynamics & KTG

The pressure ' P ', volume ' V ' and temperature ' T ' of a gas in a jar ' A ' and the gas in other jar ' B ' is at pressure ' 2 P ', volume ' V ' and temperature ' \frac{T}{4} '. Then the ratio of the number of molecules in jar A and jar B will be

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