Determine the change in internal energy, of the gas during this process

In summary: I missing something?In summary, the first law of thermodynamics states that the change in internal energy, ΔE, of a gas is equal to the heat flow into the gas (ΔQ) minus the work done by the gas (W). In this specific case, the change in internal energy of the gas is 1450 kJ due to the gas being heated and compressed, with 800 kJ of heat flow into the gas and 650 kJ of work done by the gas. The correct use of signs is crucial to avoid confusion in this equation.
  • #1
new^2^physics
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Homework Statement



A gas sample heated in a cylinder used 650 kJ of heat. A piston that compresses the gas does 800 kJ of work. What is the change in internal energy, ΔE, of the gas during this process


Homework Equations



ΔE = q + w

The Attempt at a Solution



ΔE = q + w
ΔE = (650kJ) + (800 kJ)
ΔE = 1450 kJ

a result of the gas being heated and compressed, the energy of the gas increases by 1450 kJ. Is this at all correct? Or should it be -650 kJ? Thank you for your help.
 
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  • #2
Hi new^2^physics, welcome to PF. Your answer looks fine.
 
  • #3
new^2^physics said:
ΔE = q + w
ΔE = (650kJ) + (800 kJ)
ΔE = 1450 kJ

a result of the gas being heated and compressed, the energy of the gas increases by 1450 kJ. Is this at all correct? Or should it be -650 kJ?
To avoid problems, you have to use signs correctly. You should state the first law as:

[tex]\Delta Q = \Delta U + W[/tex]

where positive [itex]\Delta Q[/itex] is the heat flow INTO the gas, positive [itex]\Delta U[/itex] is the INCREASE in internal energy of the gas, and positive W is the work done BY the gas (so if work is done on the gas, W is negative).

If you make careful use of the signs (+ or -) you will avoid confusion.

In this case, you would state the first law as:

[tex]\Delta U = \Delta Q - W[/tex]

where [itex]\Delta Q = 800 J [/itex] and W = -650 J. (since work is done ON the gas).

AM
 

1. What is internal energy?

Internal energy is the total energy stored within a system, including the kinetic and potential energy of its particles.

2. What causes a change in internal energy?

A change in internal energy can be caused by changes in temperature, pressure, or volume of a system, as well as through chemical reactions or work done on the system.

3. How is the change in internal energy calculated?

The change in internal energy is calculated by subtracting the initial internal energy from the final internal energy of the system. This can be represented by the equation ∆U = U(final) - U(initial).

4. How is the change in internal energy related to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. The change in internal energy is a measure of the amount of energy transferred or converted within a system.

5. How is the change in internal energy measured?

The change in internal energy can be measured using various techniques, such as calorimetry or by measuring changes in temperature, pressure, or volume. It can also be calculated using thermodynamic equations and data from experiments.

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