# Ideal Gas Law Questions

3. How is the ideal gas law modified to account for the finite volume of molecules?

4. The temperature of the sea bed 60 m below the surface and at the surface are both 20C. A rubber balloon is inflated at the sea bed with 2.0 mole gas neglecting the works done on the rubber determine:

i)the volume of the balloon at the sea bed and ii) the volume of the balloon after it has been allowed to float slowly up to the surface.

ii) the volume of the balloon after it has been allowed to float slowly up to the surface

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#### Solution Preview

Please see the attached file.

3. How is the ideal gas law modified to account for the finite volume of molecules?

, where

• The parameter b is related to the size of each molecule. The volume that the molecules have to move around in is not just the volume of the container V, but is reduced to ( V - nb ).

• ...

#### Solution Summary

The solution shows how to use and modify the ideal gas law to account for volume and answer the following questions.

Thermal physics and Ideal gas law

Question 1: The figure below is a plot of Fahrenheit temperature versus Celsius temperature.

(a) Is the value of the y-intercept found by setting (Helpful Hint: The y-intercept is found by setting your x-value to 0. Look at the graph and determine what your x and y-axis represent.)

1. TF = TC

2. TC = 0 or

3. TF = 0?

(b) Compute the value of the y-intercept. (Helpful Hint: Slope is equal to Δy/Δx. Choose 2 points on the line (try the initial and terminal points since they are labled). Identify the x and y coordinates of each point and solve for the slope.)

(c) What would be the slope and y-intercept if the graph were plotted the opposite way (Celsius versus Fahrenheit)? . (Helpful Hint: Take the reciprocal of the value for the slope in part b)

Question 2:If 2.4 m3 of a gas initially at STP is compressed to 1.6 m3 and its temperature raised to 30oC, what is the final pressure? (Helpful Hint: P(f) = P(i)V(i)T(f)/T(i) (where i=initial and f=final).)

(see attached file for diagram)

Question 3: A driver releases an air bubble of volume 2.0 cm3 from a depth of 15 m below the surface of a lake, where the temperature is 7.0oC. What is the volume of the bubble when it reaches just below the surface of the lake, where the temperature is 20oC? (Helpful Hint: Find the pressure (P) at a depth of 15 m by (P = ρgh). Next, find the pressure at 0.078 m below the surface. Finally, use the equation V(f) = P(i)V(i)T(f)/[T(i)P(f)])

Question 4: A steel beam 10m long is installed in a structure at 20oC. What are the beam's changes in length at the temperature extremes of -30oC to 45oC? (Helpful Hint: ΔL =LoαΔT for both cases.)

Question 5: A circular steel plate of radius 0.10 m is cooled from 350oC to 20oC. By what percentage does the plate's area decrease? (Helpful Hint: Use the equation ΔA/Ao = (2α)ΔT (remember that Ao = πr^2). Multiply the result by 100 to get the percentage.)

Question 6: Will heat always flow from an object having more energy to one having less energy? Justify your answer as completely as possible, demonstrating understanding of both 'heat' and 'energy'.

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