800 kJ of heat is supplied to an ideal gas at constant pressure of $4.5\times {10}^5$ Pa . As a result the gas changes its volume from $0.5 {\mathrm{m}}^3 \mathrm{to} 2.0 {\mathrm{m}}^3$. The change in internal energy of the gas is:

P = $P=4.5 \times {10}^5 \mathrm{Pa}; \mathrm{dQ} = 800 \mathrm{kJ}$

 ${\mathrm{V}}_1 = 0.5 {\mathrm{m}}^3; {\mathrm{V}}_2 = 2{\mathrm{m}}^3$

    $\mathrm{dW} = \mathrm{P}({\mathrm{V}}_2-{\mathrm{V}}_1) = 4.5 \times {10}^5(2-0.5) \mathrm{J}$

         $=6.75 \times {10}^5 \mathrm{J}$

Change in internal energy:

 $\mathrm{dU}=\mathrm{dQ}-\mathrm{dW}$

        $=800 \times {10}^3-6.75 \times {10}^5$ 

        $=1.25 \times {10}^5 \mathrm{J}$