# Energy and work done by a gas system

An insulated cylinder closed at one end by a frictionless piston contains 20g of hydrogen gas at 30 degrees Celsius. This is heated to 40 degrees Celsius with the pressure kept constant at 1 bar and the volume increases by 7*10^-4 m^3. (The specific heat of H2 at constant pressure is 1.4*10^4 JKg^-1 K^-1).

a) What is the work done by the gas?

b) What is the change in internal energy of the system?

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#### Solution Preview

Work done by a system is defined as:

And the total work of a system starting at volume Vi and ends up with volume Vf is:

In most cases, the pressure and volume are interlinked (the pressure is a function of the volume). However, in this case the pressure is constant (isobaric process).

Thus, in the integral expression for work the pressure can be taken outside of the ...

#### Solution Summary

Energy and work done by a gas system is analyzed. A frictionless piston contains 20 g of hydrogen gas at a specific temperature. The energy of the gas as well as the change in internal energy of the system is calculated.

Total of twenty questions related to work, energy, power, simple pendulum, electricity, electric power, gravitational potential energy, kinetic energy ,Celsius temperature, Kelvin temperature, specific heat, heat and Ideal gas law.

1. A force of 7.2 N acting on a 1.0-kg object initially at rest moves it through a parallel distance of 2.5 m. How much work is done on the object?

2. Neglecting friction, what is the speed of the object in Question 1 when it has moved 2.5 m?

3. A 0.10-kg ball is dropped from a height of 10 m and rebounds to a height of 8.0 m. How much energy was lost, and what happened to it?

4. A student weighing 700 N climbs a flight of stairs 5.0 m high. Calculate the work done.

5. If the student in Question 4 climbs the stairs in 10 s, what power was required?

6. The bob of a simple pendulum is 0.50 m above the floor at its lowest position. Calculate the maximum speed of the bob when it is held at a maximum height of 2.5 m and released.

7. Given 10 kWh of electricity and assuming no losses, how much work, in joules, could be done?

8. A 5.00-kg object is lifted from the floor to a shelf. The object's new gravitational potential energy relative to the floor is 102 J. What is the height of the shelf?

9. Work in the amount of 280 J is done in lifting an object a distance of 4.0 m in a time of 7.0 s. How much power was required?

10. Car B is traveling twice as fast as Car A, but Car A has twice the mass of Car B. Which car has the greater kinetic energy and by what factor?

11. It is 23 ° F outside. What is the Celsius temperature?

12. For a temperature of − 40 ° F, what are the corresponding temperatures on the Kelvin scale?

13. When 10 kcal of heat is added to 2.0 kg of a substance, its temperature increases 20 C ° . What is the specific heat of the substance?

14. How much heat is required to melt 5.0 kg of ice at 0 ° C to water at 0 ° C?

15. How much heat is necessary to change 20 g of ice at − 10 ° C into water at 20 ° C?

16. How many kcal of heat would be needed to melt 0.12 kg of ice at 0 ° C and increase the temperature to 25 ° C?

17. A constant volume and mass of helium gas at 27 ° C is heated so that the pressure of the gas doubles. What is the new temperature of the gas in degrees Celsius?

18. The number of molecules in a container is tripled and the Kelvin temperature doubled. The volume remains unchanged. The new pressure will be how many times greater than the original pressure?

19. An ideal gas is confined to a container with an adjustable volume. If the number of molecules and temperature are held constant, by what factor will the volume change when the pressure is tripled?

20. The piston of a cylinder containing a quantity of ideal gas is advanced so that the volume of the gas is decreased by one-half. A pressure gauge on the cylinder shows the pressure of the gas to have increased threefold in the process. By what factor does the temperature of the gas change?

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