At moderate pressure the compressiblity factor of a particular gas is given by `Z=1+0.34p-170p/T` where p is in bar and T is in kelvin what will be the Boyle's temperature?

Options

A. 100K
B. 380K
C. 500K
D. 680K

Answer

To find the Boyle's temperature for the given gas, we start from the equation for the compressibility factor \( Z \):

\[ Z = 1 + 0.34p - \frac{170p}{T} \]

where \( p \) is in bar and \( T \) is in Kelvin. At Boyle's temperature, the compressibility factor \( Z \) is equal to 1.

### Step-by-Step Solution:

1. **Set the Compressibility Factor to 1**:
\[ Z = 1 \implies 1 = 1 + 0.34p - \frac{170p}{T} \]

2. **Simplify the Equation**:
Subtract 1 from both sides:
\[ 0 = 0.34p - \frac{170p}{T} \]

3. **Factor Out \( p \)**:
Since \( p \) is a common term, we can factor it out:
\[ 0 = p \left( 0.34 - \frac{170}{T} \right) \]

4. **Set the Factor to Zero**:
For the equation to hold true, either \( p = 0 \) (which is not meaningful in this context) or:
\[ 0.34 - \frac{170}{T} = 0 \]

5. **Solve for \( T \)**:
Rearranging gives:
\[ \frac{170}{T} = 0.34 \]
Multiplying both sides by \( T \) and then rearranging gives:
\[ T = \frac{170}{0.34} \]

6. **Calculate \( T \)**:
Performing the division:
\[ T = 500 \text{ K} \]

### Conclusion:
The Boyle's temperature for the gas is \( 500 \text{ K} \).