Question

80.5 J of heat are added to 0.222 moles of a diatomic gas. It expands, doing work, and the temperature goes up by 12.0 K. How much work did the gas do? (Unit=J)

Answer 1

The work done by the gas is 25.1 J

Explanation:

The change in internal energy of a diatomic gas is given by the equation

$\Delta U = \frac{5}{2}nR\Delta T$

where:

n is the number of moles

R is the gas constant

$\Delta T$ is the change in temperature

For the gas in this problem:

n = 0.222 mol

$R=8.314 J/mol K$

$\Delta T=12.0 K$

Substituting,

$\Delta U = \frac{5}{2}(0.222)(8.314)(12.0)=55.4 J$

Now we can find the work done by the gas using the 1st law of thermodynamics:

$\Delta U = Q-W$

where:

Q = +80.5 J is the heat added to the gas

$\Delta U = +55.4 J$ is the change in internal energy

W is the work done by the gas

And solving for W,

$W=Q-\Delta U = 80.5-(55.4)=25.1 J$

And since it is positive, it means that the work is done BY the gas.

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