Heat and Thermodynamics 6 Question 37
42. Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at $0^{\circ} C$ and a pressure of $76 cm$ of mercury. One of the bulbs is then placed in melting ice and the other is placed in a water bath maintained at $62^{\circ} C$. What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible.
$(1985,6$ M)
Show Answer
Answer:
Correct Answer: 42. $83.83 cm$ of $Hg$
Solution:
- Let $x$ moles transfer from bulb of higher temperature to lower temperature.
Applying $p V=n R T$ for both the bulbs initially and finally
$$ \begin{aligned} & 76 \times V=n R \times 273 \\ & p^{\prime} \times V=(n+x) R \times 273 \\ & p^{\prime} \times V=(n-x) R \times 335 \end{aligned} $$
Solving these equations, we get $n=\frac{602}{62} x$
Now, dividing Eq. (ii) with Eq. (i), we get
$$ \begin{array}{rlrl} & & \frac{p^{\prime}}{76}=\frac{n+x}{n} & =1+\frac{x}{n}=1+\frac{62}{602}=1.103 \\ \therefore & p^{\prime} & =83.83 cm \text { of } Hg \end{array} $$
