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

[new^2^physics]

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.

 

[Mapes]

Hi new^2^physics, welcome to PF. Your answer looks fine.

 

[Andrew Mason]

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:

$$\Delta Q = \Delta U + W$$

where positive $\Delta Q$ is the heat flow INTO the gas, positive $\Delta U$ 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:

$$\Delta U = \Delta Q - W$$

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

AM