C

Step 1: Use the ideal gas law and the concept of pressure as it relates to temperature in a gas thermometer. The pressure in a gas thermometer is directly proportional to the temperature in Kelvin.
Step 2: Identify the known values:
- At the triple point of water (273.16 K), the pressure is 3.0 × 10⁴ N/m².
- For the unknown system, the pressure is 3.5 × 10⁴ N/m².
Step 3: Set up the ratio of pressures and temperatures. Let T be the temperature of the unknown system in Kelvin:

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

Substituting the values, this becomes:

$\frac{3.0 \times 10^4}{273.16} = \frac{3.5 \times 10^4}{T}$
Step 4: Solve for T:
Cross-multiplying gives:

$(3.0 \times 10^4) T = (3.5 \times 10^4)(273.16)$

Now, solving for T:

$$T = \frac{(3.5 \times 10^4)(273.16)}{3.0 \times 10^4}$$

Calculating the numerical value:
Convert it to Celsius after finding T:

$$T - 273.15 = T_c \text{ (to convert K to ºC)}$$
Now compute T and find T_c.
Therefore, the answer is approximately 32.0 ºC.