I think there are several mistakes somewhere, so let's start from the beginning.

Yes, the formula to use here is \(\displaystyle Q = mc_p\Delta T\) (Use cp because the question states that the heat transfer occurs at constant pressure).

You can obtain a formula describing what you want by rearranging it to make the final temperature the subject:

\(\displaystyle Q = mc_p\Delta T\)

\(\displaystyle Q = mc_p (T_2 - T_1)\)

\(\displaystyle T_2 - T_1 = \frac{Q}{mc_p}\)

\(\displaystyle T_2 = T_1 + \frac{Q}{mc_p}\)

where \(\displaystyle T_2\) is the final temperature and \(\displaystyle T_1\) is the initial temperature.

Now... you have 19 moles of Argon gas. 1 mol of Argon gas has a mass of approximately 40g (because of the mass number on the periodic table), so 19 moles of Argon gas has a mass of \(\displaystyle 19 \times 0.04 = 0.76\) kg.

\(\displaystyle T_2 = 21 + \frac{4400}{0.76\times 520} = 21 + 11.13 = 32.13 \) degrees Celsius.