This problem involves the thermodynamic relationship of gases. Here is the step-by-step analysis and solution:

Given:

1. Mass of Oxygen ($m$) = $17 \, \text{g} = 0.017 \, \text{kg}$
2. Molecular weight of Oxygen ($M$) = $32 \, \text{g/mol}$
3. Initial temperature ($T_1$) = $37^\circ \text{C} = 310.15 \, \text{K}$
4. Initial pressure ($P_1$) = $2 \times 10^5 \, \text{N/m}^2$
5. Final pressure ($P_2$) = $4 \times 10^5 \, \text{N/m}^2$

We need to find the final temperature ($T_2$) of the gas after heating, assuming constant volume.

Step 1: Use the Ideal Gas Law Relationship at Constant Volume

The equation for a gas under constant volume is:

$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Rearranging for $T_2$:

$T_2 = T_1 \cdot \frac{P_2}{P_1}$

Step 2: Substitute Known Values

$T_2 = 310.15 \, \text{K} \cdot \frac{4 \times 10^5}{2 \times 10^5}$

Simplify:

$T_2 = 310.15 \, \text{K} \cdot 2 = 620.30 \, \text{K}$

Convert back to Celsius:

$T_2 = 620.30 - 273.15 = 347.15^\circ \text{C}$

Final Answer:

The final temperature of the oxygen gas after heating is:

$\boxed{347.15^\circ \text{C}}$

Would you like further clarification or additional calculations?

Related Questions:

1. What assumptions are made when applying the ideal gas law here?
2. How would the calculation differ if the volume were not constant?
3. What is the change in internal energy for the gas if it behaves ideally?
4. How does the mass of the gas affect the temperature change under these conditions?
5. Can we calculate the number of moles of oxygen in this scenario?

Tip:

Always double-check units for consistency in thermodynamic equations—especially temperature in Kelvin!