The molar heat capacity of a certain substance varies with temperature according to the given equation
`C=27.2+(4xx10^-3)T`
The heat necessary to change the temperature of 2 mol of the substance from 300 K to 700 K is

Options

A. `3.46xx10^4J`
B. `2.33xx10^3J`
C. `3.46xx10^3J`
D. `2.33xx10^4J`

Explanation

To solve the problem, we need to calculate the heat necessary to change the temperature of 2 moles of a substance from 300 K to 700 K, given the molar heat capacity equation \( C = 27.2 + 4 \times 10^{-3} T \).

### Step-by-Step Solution:

1. **Identify the Variables:**
- Moles of substance, \( n = 2 \) mol
- Initial temperature, \( T_1 = 300 \) K
- Final temperature, \( T_2 = 700 \) K
- Molar heat capacity, \( C(T) = 27.2 + 4 \times 10^{-3} T \)

2. **Set Up the Heat Equation:**
The heat \( Q \) required to change the temperature can be expressed as:
\[ Q = n \int_{T_1}^{T_2} C(T) \, dT \]
Here, \( C(T) \) is the molar heat capacity which varies with temperature.

3. **Substitute the Molar Heat Capacity into the Integral:**
\[ Q = 2 \int_{300}^{700} \left( 27.2 + 4 \times 10^{-3} T \right) \, dT \]

4. **Break Down the Integral:**
\[ Q = 2 \left( \int_{300}^{700} 27.2 \, dT + \int_{300}^{700} 4 \times 10^{-3} T \, dT \right) \]

5. **Calculate the First Integral:**
\[ \int_{300}^{700} 27.2 \, dT = 27.2 \times (700 - 300) = 27.2 \times 400 = 10880 \]

6. **Calculate the Second Integral:**
\[ \int_{300}^{700} 4 \times 10^{-3} T \, dT = 4 \times 10^{-3} \left[ \frac{T^2}{2} \right]_{300}^{700} \]
\[ = 4 \times 10^{-3} \left( \frac{700^2}{2} - \frac{300^2}{2} \right) = 4 \times 10^{-3} \left( \frac{490000 - 90000}{2} \right) \]
\[ = 4 \times 10^{-3} \left( \frac{400000}{2} \right) = 4 \times 10^{-3} \times 200000 = 800 \]

7. **Combine the Results:**
\[ Q = 2 \left( 10880 + 800 \right) = 2 \times 11680 = 23360 \, \text{J} \]

8. **Final Answer:**
\[ Q = 2.336 \times 10^4 \, \text{J} \]

### Conclusion:
The heat necessary to change the temperature of 2 moles of the substance from 300 K to 700 K is approximately \( 2.33 \times 10^4 \, \text{J} \).