Five moles of an ideal monatomic gas with an initial temperature of 126 ∘c expand and, in the process, absorb an amount of heat equal to 1300 j and do an amount of work equal to 2080 j .

Missing question:
"What is the final temperature of the gas?"

Solution:
The first law of thermodynamics states that:

where
is the variation of internal energy of the gas
 is the heat absorbed by the gas
is the work done by the gas

The gas in this problems absorbs  of heat and it does  of work, so its variation of internal energy is:

This means the gas has lost internal energy.

But the variation of internal energy is related to the variation of temperature by:

where
k is the number of degrees of freedom (k=3 for a monoatomic gas)
n is the number of moles
R is the gas constant
is the variation of temperature of the gas.

Re-arranging the equation and using the variation of internal energy that we found at the previous step, we find:


Variation of temperatures in Kelvin are equal to variation of temperatures in Celsius, so  and we can now find the final temperature of the gas:

    5.5 n======    assuming that      we have      m = 0.145 kg    a = 38 m/s²therefore    5.51 n, but two significant figures.final answer: 5.5 n

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