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Home / what is the change in internal energy of the gas? express your answer to three significant figures.

what is the change in internal energy of the gas? express your answer to three significant figures.

Learning Objectives

  1. Define a type of work in terms of pressure and book.
  2. Define heat.
  3. Relate the corporeality of heat to a temperature change.

We take already divers work as a force acting through a distance. It turns out that there are other equivalent definitions of work that are also important in chemistry.

When a sure volume of a gas expands, it works against an external force per unit area to expand (Figure 7.2 "Volume versus Pressure"). That is, the gas must perform work. Assuming that the external pressure P ext is constant, the corporeality of work done past the gas is given past the equation

west = −P ext × ΔV

where ΔFive is the change in volume of the gas. This term is e'er the concluding volume minus the initial volume,

ΔV =V final − V initial

and can be positive or negative, depending on whether V last is larger (is expanding) or smaller (is contracting) than V initial. The negative sign in the equation for work is important and implies that every bit volume expands (Δ5 is positive), the gas in the system is losing energy as piece of work. On the other hand, if the gas is contracting, Δ5 is negative, and the two negative signs make the work positive, so energy is existence added to the system.

Figure 7.ii Volume versus Pressure

Volume vs Pressure

When a gas expands against an external force per unit area, the gas does work.

Finally, let us consider units. Volume changes are usually expressed in units like liters, while pressures are usually expressed in atmospheres. When we employ the equation to decide work, the unit for piece of work comes out as liter·atmospheres, or Fifty·atm. This is not a very common unit for piece of work. Notwithstanding, there is a conversion factor between 50·atm and the common unit of work, joules:

1 50·atm = 101.32 J

Using this conversion gene and the previous equation for work, we tin calculate the work performed when a gas expands or contracts.

Case ii

What is the piece of work performed by a gas if it expands from 3.44 Fifty to half dozen.xix L against a constant external pressure of one.26 atm? Express the final answer in joules.

Solution

Beginning we demand to decide the change in volume, ΔFive. A change is always the last value minus the initial value:

ΔFive =V final − V initial = six.19 L − 3.44 50 = ii.75 L

At present nosotros can use the definition of work to determine the work washed:

w = −P ext · ΔV = −(1.26 atm)(2.75 L) = −3.47 L·atm

Now we construct a conversion factor from the human relationship between liter·atmospheres and joules:

_347

We limit the final answer to iii significant figures, as appropriate.

Test Yourself

What is the piece of work performed when a gas expands from 0.66 Fifty to ane.33 L against an external pressure of 0.775 atm?

Respond

−53 J

Heat is another aspect of energy. Heat is the transfer of energy from one torso to another due to a difference in temperature. For example, when we touch something with our easily, we interpret that object equally either hot or cold depending on how free energy is transferred: If energy is transferred into your hands, the object feels hot. If energy is transferred from your hands to the object, your easily feel cold. Because heat is a measure out of energy transfer, rut is also measured in joules.

For a given object, the amount of heat (q) involved is proportional to two things: the mass of the object (m) and the temperature change (ΔT) evoked by the energy transfer. Nosotros can write this mathematically as

q∝m × ΔT

where ∝ ways "is proportional to." To make a proportionality an equality, we include a proportionality constant. In this instance, the proportionality constant is labelled c and is chosen the specific heat capacity, or, more succinctly, specific rut:

q = mcΔT

where the mass, specific estrus, and alter in temperature are multiplied together. Specific heat is a measure out of how much free energy is needed to change the temperature of a substance; the larger the specific oestrus, the more energy is needed to change the temperature. The units for specific heat are Jg⋅°C or Jg⋅Thousand, depending on what the unit of ΔT is. You may note a difference from the insistence that temperature be expressed in Kelvin. That is because a alter in temperature has the aforementioned value whether the temperatures are expressed in degrees Celsius or kelvins.

Case 3

Calculate the estrus involved when 25.0 one thousand of Iron increase temperature from 22°C to 76°C. The specific heat of Fe is 0.449 J/g·°C.

Solution

Offset nosotros need to decide ΔT. A change is always the final value minus the initial value:

ΔT = 76°C − 22°C = 54°C

Now we can use the expression for q, substitute for all variables, and solve for estrus:

q250

Note how the g and °C units cancel, leaving J, a unit of heat. Also note that this value of q is inherently positive, significant that energy is going into the organisation.

Test Yourself

Calculate the estrus involved when 76.v g of Ag increment temperature from 17.viii°C to 144.5°C. The specific heat of Ag is 0.233 J/yard·°C.

Respond

2,260 J

As with whatever equation, when you lot know all simply one variable in the expression for q, you tin can determine the remaining variable by using algebra.

Case iv

It takes five,408 J of heat to raise the temperature of 373 g of Hg by 104°C. What is the specific heat of Hg?

Solution

We tin can showtime with the equation for q, but now unlike values are given, and nosotros need to solve for specific estrus. Annotation that ΔT is given direct as 104°C. Substituting,

5,408 J = (373 g)c(104°C)

Nosotros divide both sides of the equation past 373 g and 104°C:

c5408

Combining the numbers and bringing together all the units, we get

c0139

Test Yourself

Gold has a specific heat of 0.129 J/g·°C. If 1,377 J are needed to increment the temperature of a sample of gilt by 99.9°C, what is the mass of the aureate?

Answer

107 m

Table vii.1 "Specific Heats of Various Substances" lists the specific heats of some substances. Specific heat is a concrete holding of substances, so it is a feature of the substance. The general thought is that the lower the specific estrus, the less free energy is required to change the temperature of the substance past a sure amount.

Table 7.1 Specific Heats of Diverse Substances

Substance Specific Heat (J/1000·°C)
water four.184
iron 0.449
gold 0.129
mercury 0.139
aluminum 0.900
ethyl alcohol two.419
magnesium 1.03
helium five.171
oxygen 0.918

Key Takeaways

  • Piece of work can be defined equally a gas irresolute volume against a constant external pressure.
  • Rut is the transfer of energy due to temperature differences.
  • Rut can be calculated in terms of mass, temperature alter, and specific oestrus.

Exercises

  1. Give two definitions of piece of work.

  2. What is the sign on work when a sample of gas increases its book? Explain why piece of work has that sign.

  3. What is the work when a gas expands from iii.00 L to 12.threescore L against an external force per unit area of 0.888 atm?

  4. What is the work when a gas expands from 0.666 L to 2.334 L against an external pressure of ii.07 atm?

  5. What is the work when a gas contracts from three.45 L to 0.97 L under an external pressure of 0.985 atm?

  6. What is the work when a gas contracts from 4.66 50 to 1.22 L under an external pressure level of three.97 atm?

  7. Similar piece of work, the sign on heat can be positive or negative. What is happening to the total free energy of a organisation if heat is positive?

  8. Like work, the sign on rut can be positive or negative. What is happening to the total energy of a system if heat is negative?

  9. What is the oestrus when 55.6 g of Iron increment temperature from 25.6°C to 177.9°C? The estrus capacity of Atomic number 26 is in Table 7.i "Specific Heats of Various Substances".

  10. What is the heat when 0.444 g of Au increases temperature from 17.eight°C to 222.5°C? The oestrus capacity of Au is in Tabular array 7.1 "Specific Heats of Diverse Substances".

  11. What is the rut when 245 yard of H2O cool from 355 M to 298 K? The estrus capacity of HiiO is in Table vii.1 "Specific Heats of Various Substances".

  12. What is the heat when 100.0 one thousand of Mg cool from 725 K to 552 K? The estrus capacity of Mg is in Table vii.1 "Specific Heats of Various Substances".

  13. It takes 452 J of heat to raise the temperature of a 36.8 g sample of a metallic from 22.9°C to 98.ii°C. What is the heat capacity of the metal?

  14. It takes 2,267 J of estrus to raise the temperature of a 44.five g sample of a metal from 33.nine°C to 288.three°C. What is the heat capacity of the metallic?

  15. An experimenter adds 336 J of heat to a 56.2 g sample of Hg. What is its alter in temperature? The heat chapters of Hg is in Table 7.1 "Specific Heats of Various Substances".

  16. To a 0.444 g sample of HtwoO, 23.4 J of oestrus are added. What is its modify in temperature? The heat chapters of H2O is in Table vii.1 "Specific Heats of Various Substances".

  17. An unknown mass of Al absorbs 187.ix J of rut and increases its temperature from 23.five°C to 35.6°C. What is the mass of the aluminum? How many moles of aluminum is this?

  18. A sample of He goes from 19.iv°C to 55.9°C when 448 J of free energy are added. What is the mass of the helium? How many moles of helium is this?

Answers

one.

Piece of work is a force interim through a altitude or a volume irresolute against some force per unit area.

three.

−864 J

5.

248 J

7.

When oestrus is positive, the total free energy of the system is increasing.

ix.

3.80 × xthree J

eleven.

−58,400 J

13.

0.163 J/yard·°C

15.

43.0°C

17.

17.iii k; 0.640 mol

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Source: https://courses.lumenlearning.com/suny-introductory-chemistry/chapter/work-and-heat/