Question

A certain amount of gas is in the glass tube shown below. The temperature of gas is $300\text{K}$. What will be the length of gas tube if temperature is doubled isobarically (Assume the area of the tube does not vary with temperature)

• A. $h=2.5\text{cm}$
• B. $h=10\text{cm}$
• C. $h=5\text{cm}$
• D. $h=7.5\text{cm}$

Answer 1

The correct option is B $h=10\text{cm}$

Given, $T_i=300\text{K};T_f=600\text{K}{h}_i=5\text{cm}$

From, ideal gas equation,

$PV=nRT$

In isobaric process, $P=\text{constant}$
Here, $n$ will be also constant.

$\therefore V\propto T$

Let the area of cross-section of glass be $A$

$\Rightarrow \frac{A{h}_i}{A{h}_f}=\frac{T_i}{T_f}$

$\Rightarrow \frac{5}{h_f}=\frac{300}{600}$

$\Rightarrow h=10\text{cm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.