To calculate the amount of heat required to raise the temperature of the same mass of oxygen through 1°C at constant pressure, you can use the formula:
\[ q = mc_p\Delta T \]
Where:
- \( q \) is the heat required
- \( m \) is the mass of the substance (1 kg in this case)
- \( c_p \) is the specific heat capacity at constant pressure (which you can find using the molar specific heat capacity \( c_p = R + c_v \), where \( c_v \) is the specific heat capacity at constant volume)
- \( \Delta T \) is the change in temperature (1°C in this case)
Given that \( R = 8.31 \, \text{J/mol.K} \), you can find \( c_v \) using the given information that 656 J of heat is required for a 1°C rise in temperature at constant volume:
\[ c_v = \frac{q}{m \Delta T} \]
Then, calculate \( c_p \):
\[ c_p = R + c_v \]
Finally, use the calculated \( c_p \) to find the heat required at constant pressure:
\[ q = mc_p\Delta T \]
Substitute the values into these equations to find the answer.