Determine the quantity of heat added to 3.5 moles of the ideal gas argon if the temperature increases from `75 ^@ C ` to `225^@ C ` during an isobaric process .
(the molar specific of argon are ` C_v = 3.0 cal // K mol ` and ` C_P = 5.0 cal // K mol ) `

Options

A. 2600 cal
B. 1600 cal
C. 21 00 cal
D. 1100 cal

Answer

To determine the quantity of heat added to 3.5 moles of the ideal gas argon during an isobaric process, we can follow these steps:

### Step 1: Understand the Isobaric Process
In an isobaric process, the pressure remains constant. The heat added to the system can be calculated using the formula:
\[ Q = n C_P \Delta T \]
where:
- \( Q \) = heat added
- \( n \) = number of moles of the gas
- \( C_P \) = molar specific heat at constant pressure
- \( \Delta T \) = change in temperature

### Step 2: Identify Given Values
From the problem, we have:
- Number of moles, \( n = 3.5 \, \text{moles} \)
- Molar specific heat at constant pressure, \( C_P = 5.0 \, \text{cal/K mol} \)
- Initial temperature, \( T_1 = 75^\circ C \)
- Final temperature, \( T_2 = 225^\circ C \)

### Step 3: Calculate the Change in Temperature
Convert the temperatures from Celsius to Kelvin (though it is not necessary for the calculation of \(\Delta T\) since the change will be the same in both scales):
\[ \Delta T = T_2 - T_1 = 225^\circ C - 75^\circ C = 150^\circ C \]

### Step 4: Substitute Values into the Formula
Now, substitute the known values into the heat formula:
\[ Q = n C_P \Delta T \]
\[ Q = 3.5 \, \text{moles} \times 5.0 \, \text{cal/K mol} \times 150 \, \text{K} \]

### Step 5: Perform the Calculation
Now, calculate \( Q \):
\[ Q = 3.5 \times 5.0 \times 150 \]
\[ Q = 3.5 \times 750 \]
\[ Q = 2625 \, \text{cal} \]

### Step 6: Conclusion
The quantity of heat added to the system is:
\[ Q = 2625 \, \text{cal} \]

### Step 7: Identify the Closest Option
The closest answer to our calculated value is 2600 calories, which is likely the correct option in a multiple-choice setting.

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