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Q. 78

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 547

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Short Answer

A beaker with a metal bottom is filled with of water at . It is brought into good thermal contact with a container holding of a monatomic gas at pressure. Both containers are well insulated from their surroundings.

What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome.

The gas pressure after a long time has elapsed is

See the step by step solution

Step by Step Solution

Step 1: Given Information

Amount of water in beaker

Temperature

Weight of container

Amount of monatomic gas

Pressure

Step 2: Explanation

According to this definition, the specific heat of a substance is the amount of energy that it requires to raise the temperature of a unit mass of the substance by .
Temperature change of a substance as a function of the amount of heat required.

Here,

is the mass of the substance, is the specific heat capacity of the substance,

the initial temperature of the substance, and is the final temperature of the substance.

Based on the ideal gas equation,

Modify the terms of

Step 3: Explanation

Substitute the values of

for

for

for

And for in the equation.

A water system and a gas system interact here. The equilibrium of a closed system depends on the transfer of heat between interacting systems.

Here,

Specific heat at constant volume

Final temperature of both the gas and water.

Convert the unit of mass from to

Step 4: Explanation

Convert the unit of temperature from to

Modify the equation (1) in terms of

Substitute the values of:

for ,

for ,

for ,

for ,

for ,

And for

Step 5: Explanation

Calculate the final pressure of the gas by using the ideal gas equation.

Substitute for ,

And

Step 3: Final Answer

Hence, the gas pressure after long time elapsed is

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