Finding Final Temperature in Constant Pressure Process : First Law [closed]

Question

Nitrogen at a pressure of 200 kPa and 30°C undergoes a constant pressure process with a heat addition of 1000 kJ. The mass of the air is 4 kg. Compute final temperature.

Convention: work done TO the system or heat added TO the system is +.

Given the first law: $\Delta U = mc_v(T_2 - T_1) = Q + W = 1000 - P(V_2 - V_1)$. Furthermore the relation holds:

$$\frac{V_1}{T_1} = \frac{V_2}{T_2} \rightarrow V_2 = \frac{V_1 T_2}{T_1}$$

Hence

$$T_2(mc_v + \frac{PV_1}{T_1}) = Q + mc_vT_1 + PV_1$$

Given that $c_v = 0.7448$, I can isolate for $T_1$ and get $543K$. However, the answer is $553K$. Is there a mistake in my logic? I did not significantly round anywhere in my answer

Answer 1

There is a simpler way to obtain the answer. The property you want to use here is enthalpy, not internal energy. The enthalpy is equal to the heat transfer to the system at a constant pressure and if you have the value of $c_p$ of Nitrogen, you can easily calculate the temperature difference due to the heat addition using the formula

$$\Delta H = m c_p \Delta T$$

I'm getting the same answer as you when I take $c_p$ as 1.04

So maybe, the answer is wrong or the author has made a mistake.