Question

What is the change in internal energy (in J) of a system that absorbs 0.464 kJ of heat from its surroundings and has 0.630 kcal of work done on it?

Answer 1

The change in the internal energy of the system is the sum/difference of the heat absorbed/emitted and the work done. Firstly, the units of the parameters should be converted to the joule. After converting the units of the parameters, the values of the heat energy and the work done should be added to find the value of the change in the internal energy.

Complete step-by-step solution:
From the given information, we have the data as follows.
A system that absorbs 0.464 kJ of heat from its surroundings and has 0.630 kcal of work done on it.
The work done on the system is 0.630 kcal. We need to convert the unit of the work done from calorie to joule. The unit conversion from calorie to joule is computed as follows.

& w=0.247\times {{10}^{3}} \\\ & \Rightarrow w=0.247\times {{10}^{3}}\times 4184 \\\ & \therefore w=10,33,448\,J \\\ \end{aligned}$$ The change in the internal energy of the system is the sum/difference of the heat absorbed/emitted and the work done. $$\Delta E=q-(-w)$$ Substitute the values of the heat and work done in the above equation. $$\begin{aligned} & \Delta E=0.615\times {{10}^{3}}-(-1033448) \\\ & \therefore \Delta E=615+1033448 \\\ \end{aligned}$$ Therefore, the value of the change in the internal energy is, $$\therefore \Delta E=10,34,063\,J$$ $$\therefore $$ The change in the internal energy (in J) of a system that absorbs 0.464 kJ of heat from its surroundings and has 0.630 kcal of work done on it is 10,34,063 J. **Note:** We need to convert the unit of the work done from calorie to joule, as the total change in the internal energy should be represented in any one of the units. One calorie equals 4184 Joule, so, we have to multiply the calorie value by 4184 to convert the unit.