The change in internal energy of the gas is -9 J
Explanation:
First of all, we need to calculate the amount of work done by the gas. This is given by the equation:
[tex]W=p(V_f - V_i)[/tex]
where
[tex]p=1.2\cdot 10^5 Pa[/tex] is the gas pressure
[tex]V_f = 0.0003 m^3[/tex] is the final volume of the gas
[tex]V_i = 0.0006 m^3[/tex] is the initial volume of the gas
Substituting, we find:
[tex]W=(1.2\cdot 10^5)(0.0003-0.0006)=-36 J[/tex]
Now we can apply the 1st law of thermodynamics to calculate the change in internal energy of the gas:
[tex]\Delta U = Q - W[/tex]
where
[tex]\Delta U[/tex] is the change in internal energy of the gas
Q = -45 J is the heat released by the gas (negative because it is given off bu the system)
W = -36 J is the work done by the gas (negative because it is done by the surrounding on the gas)
Substituting, we find:
[tex]\Delta U = -45 - (-36) = -9 J[/tex]
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