Answer:
a) [tex] \Delta U = 7.5 kJ [/tex]
b) [tex]T_{f} = 900 K [/tex]
Explanation:
a) To find the change in its internal energy (U) we need to use the following equation:
[tex] \Delta U = W + Q [/tex]
Where:
W: is the work done on the system
Q: is the energy transferred into the system by heat = 12.5 kJ
Since we have an isobaric expansion, the work is:
[tex] W = - P\Delta V = - P(V_{f} - V_{i}) [/tex]
Where:
[tex]V_{f}[/tex]: is the final volume = 3.00 m³
[tex]V_{i}[/tex]: is the initial volume = 1.00 m³
P: is the pressure = 2.50 kPa
[tex] W = -P(V_{f} - V_{i}) = -2.5 \cdot 10^{3} Pa(3.00 m^{3} - 1.00 m^{3}) = -5.00 \cdot 10^{3} J [/tex]
Now, we can find the change in its internal energy:
[tex] \Delta U = W + Q = -5.00 \cdot 10^{3} J + 12.5 \cdot 10^{3} J = 7.5 \cdot 10^{3} J [/tex]
b) The final temperature can be found as follows:
[tex] \frac{V_{i}}{V_{f}} = \frac{T_{i}}{T_{f}} [/tex]
[tex] T_{f} = \frac{T_{i}*V_{f}}{V_{i}} = \frac{300 K*3.00 m^{3}}{1.00 m^{3}} = 900 K [/tex]
Hence, the final temperature is 900 K.
I hope it helps you!
