Answer:
Constant Specific Heats: [tex]Q_{in} = 43.08 kJ[/tex], Non-Constant Specific Heats: [tex]Q_{in} = 43.17 kJ[/tex]
Explanation:
By using the First Law of Thermodynamics, it is to notice the inexistence of work interactions due to the rigidness of the container, as well as the absence of mass interactions since it is sealed. In consequence, the equation is simplified to this form:
[tex]Q_{in} = U_{f} - U_{o}[/tex]
Below is the summary of calculation for the cases of constant and non-constant specific heats:
Constant Specific Heats
Previous expresion can be re-written to:
[tex]Q_{in} = m \cdot c_{v} \cdot \Delta T\\Q_{in} = (1 kg) \cdot (0.718 \frac{kJ}{kg \cdot K})\cdot (60 K)\\Q_{in} = 43.08 kJ[/tex]
Non-Constant Specific Heats
[tex]Q_{in} = m \cdot (u_{f} - u_{o})\\Q_{in} = (1 kg) \cdot (257.24 \frac{kJ}{kg} - 214.07 \frac{kJ}{kg})\\Q_{in} = 43.17 kJ[/tex]
