Concept:To determine how pressure responds to simultaneous changes in both temperature and volume, we use the combined gas law.
Formula:$$ P = \frac{nRT}{V} \quad \text{or} \quad \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} $$
Solution:- Let initial state be: Pressure = \( P \), Volume = \( V \), Temperature = \( T \). (Assuming moles, n, is constant).
- The temperature is doubled: New Temperature = \( 2T \).
- The volume is doubled: New Volume = \( 2V \).
- Plug these into the ideal gas rearranged for new pressure \( (P_{new}) \):
- \( P_{new} = \frac{nR(2T)}{(2V)} \).
- The '2' in the numerator and the '2' in the denominator cancel each other out completely.
- \( P_{new} = \frac{nRT}{V} = P_{original} \).
- Therefore, the pressure remains exactly unchanged. The expansion of volume perfectly negates the increase in kinetic energy from the temperature.
Why other options are incorrect:- Options A, B, & D: Mathematical derivation proves the effects precisely cancel out, leaving no net change.
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