Question

When 300 J of heat is given to an ideal gas with \( C_p = \frac{7}{2}R \), its temperature rises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) ______ g. (R = 8.314 J/mol K)

Hint:

At constant volume, always use \(C_v\) instead of \(C_p\).

Answer 1

Correct Answer: 4

Step 1: Find \(C_v\) from given \(C_p\).
For an ideal gas, \[ C_p - C_v = R \] \[ C_v = C_p - R = \frac{7}{2}R - R = \frac{5}{2}R \]
Step 2: Write heat equation at constant volume.
\[ Q = n C_v \Delta T \]
Step 3: Convert temperature change into Kelvin.
\[ \Delta T = 50 - 20 = 30\,\text{K} \]
Step 4: Substitute given values.
\[ 300 = n \times \frac{5}{2} \times 8.314 \times 30 \] \[ n \approx 0.48\,\text{mol} \]
Step 5: Calculate mass of gas.
Molar mass of gas \[ M = \frac{C_p}{C_p - C_v} \times R = 28\,\text{g/mol (approximately)} \] \[ \text{Mass} = nM \approx 0.48 \times 28 \approx 4\,\text{g} \]