# During compression of a spring the work done is $10\:kJ\:\:and\:\:2\:kJ$  escaped to the surrounding as heat . The change in internal energy , $\Delta U(in\:\:kJ)$   is : Option 1) $-12$ Option 2) $-8$ Option 3) $8$ Option 4) $12$

Internal Energy -

Fo an ideal gas E is a function of temperature only

$\Delta E= K.E_{Translational}+K.E_{Rotational }+K.E_{vibrational}$

- wherein

With change in temperature only kinetic energy is changed but not any potential energy.

First law of Thermodynamics -

Energy of universe is always conserved or total energy of an isolated system is always conserved

$\Delta E= q + W$

- wherein

$\Delta E=$ Internal Energy

$q=$ Heat

$W=$ work

we know ,

$\\ \Delta U=q+w\\\\\:w=10\:\:kJ(positive\:\:compression)$

$\\ q=-2\:KJ(negative,\:heat\:\:released/escaped)\\\\\:\Delta V=-2+10=8\:\:KJ$

Option 1)

$-12$

Option 2)

$-8$

Option 3)

$8$

Option 4)

$12$

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