For constant volume processes the heat capacity of gas A is greater than the heat capacity of gas B. We conclude that when they both absorb the same energy as heat at constant volume

Options

A. the temperature of A increase more than the temperature of B.
B. the temperature of B increases more than the temperature of A.
C. the internal energy of A increases more than the internal energy of B.
D. the internal energy of B increases more than the internal energy of A.

Answer

To solve the problem, we need to analyze the relationship between heat capacity, heat transfer, and temperature change for two gases, A and B, under constant volume conditions.

### Step-by-Step Solution:

1. **Understanding Heat Capacity**:
- Heat capacity at constant volume (C_v) is defined as the amount of heat required to raise the temperature of a substance by one degree Celsius (or one Kelvin) at constant volume.
- Mathematically, it is expressed as:
\[ Q = C_v \Delta T \]
where \( Q \) is the heat added, \( C_v \) is the heat capacity, and \( \Delta T \) is the change in temperature.

2. **Given Information**:
- We know that the heat capacity of gas A (\( C_{vA} \)) is greater than the heat capacity of gas B (\( C_{vB} \)):
\[ C_{vA} > C_{vB} \]

3. **Same Heat Absorption**:
- Both gases absorb the same amount of heat energy \( Q \) at constant volume:
\[ Q_A = Q_B = Q \]

4. **Temperature Change Calculation**:
- For gas A:
\[ Q = C_{vA} \Delta T_A \implies \Delta T_A = \frac{Q}{C_{vA}} \]
- For gas B:
\[ Q = C_{vB} \Delta T_B \implies \Delta T_B = \frac{Q}{C_{vB}} \]

5. **Comparing Temperature Changes**:
- Since \( C_{vA} > C_{vB} \), it follows that:
\[ \Delta T_A < \Delta T_B \]
- This means that the temperature change for gas A is less than that for gas B when both absorb the same amount of heat.

6. **Conclusion**:
- Therefore, if both gases absorb the same amount of heat at constant volume, the temperature of gas A will increase less than the temperature of gas B:
\[ T_A \text{ increases less than } T_B \]

### Final Answer:
The temperature of gas B increases more than the temperature of gas A when both absorb the same energy as heat at constant volume.