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Q. 53

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 545

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Short Answer

A diameter cylinder contains argon gas at pressure and a temperature of . A piston can slide in and out of the cylinder. The cylinder's initial length is of heat are transferred to the gas, causing the gas to expand at constant pressure. What are (a) the final temperature and (b) the final length of the cylinder?

a) The final temperature is

b) The final length of the cylinder is

See the step by step solution

Step by Step Solution

Step 1: Given Information (Part a)

Diameter of the cylinder is

Pressure

Cylinder Initial length

Temperature

Step 2: Explanation (Part a)

(a) Since the process is isothermic, the heat exchanged will be given as a function of the temperature change by,

Therefore, the temperature difference will be

Here we don't know the number of moles, but again, we shouldn't calculate it numerically, but instead substitute its parametric expression.

From the ideal gas law, we can find to be

Surely enough, when substituting we have to substitute all belonging to the same state.

Substituting, we can find the temperature difference to be

Therefore, the temperature will be

Step 3: Explanation (Part a)

If unconvinced, one can perform dimensional analysis to confirm our expression.

In our situation, we are given the diameter of the cylinder and the initial height, not the initial volume.

Therefore, we can write

Substituting in the expression we found for the temperature, we have

In our given numerical case, we will have

Step 4: Final Answer (Part a)

Therefore, the final temperature is

Step 5: Given Information (Part b)

Diameter of the cylinder is

Pressure

Cylinder Initial length

Temperature

Step 6: Explanation (Part a)

Since the process is isobaric, we can write

The volume, however, as we mentioned, is .

Substituting and then cancelling the cross-section areas we get

In our numerical case, we will have

Step 7: Final Answer (Part b)

Therefore, final length of the cylinder is

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