# Insulated bulbs immersed in heat reserviors

• decentfellow
In summary, the pressure in the bulbs is increased by 3.2 cm of mercury when they are placed in the melting ice and water reservoirs.
decentfellow

## Homework Statement

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\text{ cm}## of mercury. One of the bulbs is then placed in melting ice and the other is placed in water at ##62^{\circ}C##. What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible.

## Homework Equations

$$PV=nRT$$

## The Attempt at a Solution

I am not sure how to attempt this question a little hint would be helpful. But, still I will show my work.

Since the bulbs are immersed in different reservoirs having different temperatures, so the temperature in both the bulbs can be simply found out by the ideal gas equation. Let the bulb immersed in the melting ice reservoir be bulb 1 and the other one be bulb 2.

So, the pressure in the bulb 1 remains unchanged since the bulb was initially at ##0^{\circ}C## and the reservoir in which it is kept is also at the same temperature.

While for bulb 2 it is kept in a reservoir which has a temperature higher than its initial temperature. As the volume of the bulb remains constant so the pressure in bulb 2 is

$$\dfrac{{(P_2)}_{i}}{{(P_2)}_{f}}=\dfrac{{(T_2)}_{i}}{{(T_2)}_{f}}\implies {(P_2)}_{f}\approx 93.2\text{ cm of Hg}$$.
But I don't feel that this is correct (not only due to the fact that the book gives a different answer) as there will be some heat conduction through the rod connecting the two bulbs. But again due to the reservoirs supplying the constant temperature indefinitely(that's what I think reservoirs do) then...I am really confused.

The book tells that the gaseous molecules rearrange themselves in such a manner so that there is mechanical equilibrium. Hence the temperature in the bulbs is not the same throughout but gradually decreases from ##T_2## (temperature of hot reservoir) to ##T_1## (temperature of cold reservoir).

Now, how was I supposed to take the hint that the system was supposed to be in mechanical equilibrium.

decentfellow said:
Now, how was I supposed to take the hint that the system was supposed to be in mechanical equilibrium.
The connecting tube is hollow. Gas can freely flow through it. As long as the pressure in the two bulbs is different, what happens?

If the pressure is unequal in the two bulbs, gas will flow from the high-pressure region to the low until pressure is equalised. Obvious when you think about it.
Now assume the pressure is equalised at 76 cm Hg. How many moles of gas are in each bulb (as a multiple of V, it will cancel). How many moles in total? How does this compare with the initial value of total moles? How do you have to adjust the pressure to get these two values equal?

## 1. What is the purpose of using insulated bulbs immersed in heat reservoirs?

The purpose of using insulated bulbs immersed in heat reservoirs is to maintain a constant temperature within the bulb. This is important for experiments or processes that require a specific temperature to be maintained.

## 2. How do insulated bulbs immersed in heat reservoirs work?

Insulated bulbs immersed in heat reservoirs work by trapping heat inside the bulb, preventing it from escaping to the surrounding environment. This allows for the temperature inside the bulb to remain constant, even when the external temperature changes.

## 3. What are some common applications of insulated bulbs immersed in heat reservoirs?

Insulated bulbs immersed in heat reservoirs are commonly used in scientific experiments, such as in chemistry and biology labs, to maintain a specific temperature for reactions or studies. They are also used in industrial processes that require precise temperature control.

## 4. Are there different types of insulated bulbs immersed in heat reservoirs?

Yes, there are different types of insulated bulbs immersed in heat reservoirs. Some may use different materials for insulation, such as glass or plastic, and may vary in size and shape depending on the specific application.

## 5. Are there any safety concerns when using insulated bulbs immersed in heat reservoirs?

Yes, there are some safety concerns when using insulated bulbs immersed in heat reservoirs. It is important to follow proper handling and safety protocols, as the bulbs can become very hot and may break if not handled carefully. It is also important to regularly check and maintain the insulation to ensure it is still effective.

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