A 3.1-mole sample of an ideal gas is gently heated at constant temperature 290 K. The gas expands to 1.5 times its initial volume as its pressure decreases. What is the change in the internal energy of the gas? Let the ideal-gas constant R = 8.314 J/(mol • K).

3000 J

1500 J

0 J

-3000 J

0 J

Explanation:

In this process, we have an ideal gas gently heated at constant temperature.

The internal energy of an ideal gas is given by:

where

n is the number of moles of the gas

R is the gas constant

T is the absolute temperature of the gas

Therefore, the change in internal energy of a gas is given by

where is the change in temperature of the gas.

As we can see from the equation, the change in internal energy of an ideal gas depends only on the change in temperature.

In this problem, the temperature of the gas is constant:

T = 290 K

So the change in temperature is zero:

Therefore, the change in internal energy is also zero.

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