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Q. 4

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 543

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Short Answer

You need to raise the temperature of a gas by 10°C. To use the least amount of heat energy, should you heat the gas at constant pressure or at constant volume? Explain.

The gas must be heated to a constant volume to use the least amount of thermal energy.

See the step by step solution

Step by Step Solution

Step 1: Given information

Change in Temperature

of gas.

Step 2: Calculation

formula used: The change of thermal energy can be defined as:

For the case of gases, consider the equationas follows:

This means that more thermal energy is required to change the temperature when the molar specific heat is high, whereas for small molar specific heat, the thermal energy required is lower. For a molar specific heat at a constant pressure, the change of thermal energy we have:

Similarly, the change of thermal energy for a process with constant volume is:

But:

Now, isolating from equation and from equation we have:

(6)

And

(7)

Replacing and into equation we obtain:

The gas must be heated to a constant volume in order to consume the least amount of thermal energy.

According to result to use the least amount of thermal energy, the gas must be heated to constant volume.

Step:3 calculation

It's an easy computation; all you have to worry about is the unit system.

Step:4  Given information

Step:5 Explanation of solution

b) We need to determine the expression for the work on the gas at constant temperature, and we know that the differential work on a gas is provided by:

As the gas is ideal we can put the pressure in terms of volume and temperature:

Then the differential work is given by:

By integrating the expression, we can calculate the work on the gas:

Then the work is given by:

Step: 6 Calculation

It's a simple calculation; the only thing to consider is the unit system.

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