Question

The change in internal energy when 20 g of a gas is heated from $ 25^\circ C $ to $ 35^\circ C $ at constant volume is: Options:

• A. \( 74 \, \text{J} \)
• B. \( 336 \, \text{J} \)
• C. \( 136 \, \text{J} \)
• D. \( 168 \, \text{J} \)

Hint:

The change in internal energy for a substance at constant volume is given by the formula \( \Delta U = m C_v \Delta T \), where \( C_v \) is the specific heat at constant volume. Always ensure proper unit conversions.

Answer 1

The Correct Option is D

We are given:
Mass of the gas, \( m = 20 \, \text{g} \)
Initial temperature, \( T_1 = 25^\circ C \)
Final temperature, \( T_2 = 35^\circ C \)
Specific heat capacity of the gas at constant volume, \( C_v = 0.2 \, \text{cal} \, \text{g}^{-1} \, \text{°C}^{-1} \)
Conversion factor: \( 1 \, \text{cal} = 4.2 \, \text{J} \)
Step 1: Change in temperature.
The temperature change \( \Delta T \) is: \[ \Delta T = T_2 - T_1 = 35^\circ C - 25^\circ C = 10^\circ C \] Step 2: Calculate the heat energy in calories.
The formula for calculating the heat energy at constant volume is: \[ Q_{\text{cal}} = m C_v \Delta T \] Substituting the given values: \[ Q_{\text{cal}} = 20 \times 0.2 \times 10 = 40 \, \text{cal} \] Step 3: Convert the energy to joules.
Since \( 1 \, \text{cal} = 4.2 \, \text{J} \), we can convert the energy from calories to joules: \[ Q_{\text{J}} = 40 \times 4.2 = 168 \, \text{J} \] Final Answer: \[ \boxed{168 \, \text{J}} \]