As a result of the isobaric change by 80 K, one mole of a certain ideal gas obtain an amount of heat equal to 1.60 kJ.
What is value of `C_(P)(JK^(-1))`?

Options

A. 1.6
B. 16
C. 20
D. 2

Explanation

To solve the problem, we need to find the value of \( C_P \) (heat capacity at constant pressure) for one mole of an ideal gas given the heat absorbed during an isobaric process.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The process is isobaric (constant pressure).
- The temperature change (\( \Delta T \)) is 80 K.
- The heat absorbed (\( Q \)) is 1.60 kJ.

2. **Convert Heat from kJ to J**:
- Since \( Q \) is given in kilojoules, we convert it to joules:
\[ Q = 1.60 \, \text{kJ} = 1.60 \times 10^3 \, \text{J} = 1600 \, \text{J} \]

3. **Use the Formula for Heat Capacity at Constant Pressure**:
- The relationship between heat absorbed, heat capacity at constant pressure, and temperature change is given by:
\[ C_P = \frac{Q}{\Delta T} \]
where \( C_P \) is the heat capacity at constant pressure, \( Q \) is the heat absorbed, and \( \Delta T \) is the change in temperature.

4. **Substitute the Values**:
- Now, substituting the values into the formula:
\[ C_P = \frac{1600 \, \text{J}}{80 \, \text{K}} \]

5. **Calculate \( C_P \)**:
- Performing the division:
\[ C_P = 20 \, \text{J/K} \]

### Final Answer:
The value of \( C_P \) is **20 J/K**.

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