# 100 g of water is heated from 30°C to 50°C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J kg -1K-1) Option 1) $4.2\: kJ$ Option 2) $8.4\: kJ$ Option 3) $84\: kJ$ Option 4) $2.1\: kJ$

As we learnt in

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.

$\\ \Delta Q= ms\Delta t\\ \Delta Q = 100\times 10^{-3}\times 4.184\times10^3\times20 = 8.4\times10^{3} \\ \Delta Q = 8.4KJ.\\ \Delta W = 0 \\ \Delta U = \Delta Q+\Delta W =8.4 KJ$

Option 1)

$4.2\: kJ$

Incorrect

Option 2)

$8.4\: kJ$

Correct

Option 3)

$84\: kJ$

Incorrect

Option 4)

$2.1\: kJ$

Incorrect

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